The joint probability density of the two random variables X and Y is given by ye-v(+1) if x ≥ 0, y ≥ 0 f(x, y) = 0 else. a) Show that f(x, y) is indeed a probability density,
Answers
After considering the given data we conclude f(x, y) is not a probability density, since it does not satisfy the second condition.
To describe that f(x, y) is indeed a probability density, we have to verify that it satisfies the following two conditions:
f(x, y) is non-negative for all values of x and y.
The integral of f(x, y) over the entire plane is equal to 1.
For the joint probability density function \(f(x, y) = ye^{(-v) (+1)} if x \geq 0, y \geq 0\)and f(x, y) = 0 otherwise, we can describe that it satisfies both of these conditions as follows:
For all values of x and y, we have
\(f(x, y) = ye^{(-v) (+1)} if x \geq 0, y \geq 0 and f(x, y) = 0\) otherwise.
Then y and \(e^{(-v) (+1)}\) are both non-negative for all values of x and y, it follows that f(x, y) is non-negative for all values of x and y.
To evaluate the integral of f(x, y) over the entire plane, we can integrate f(x, y) with concerning both x and y over their entire ranges:
\(\int \int f(x, y) dxdy = \intb\int ye^{(-v)(+1)} dx dy\)
Since the function \(ye^{(-v) (+1)}\) is non-negative for all values of x and y, we can integrate it over the entire plane by integrating it over the first quadrant and then multiplying by 4:
\(\int\int ye^{(-v) (+1)} dx dy = 4\int\int ye^{(-v) (+1)} dx dy\)
\(= 4\int0\int\infty ye^{(-v) (+1)} dx dy\)
\(= 4\int0\infty y \int0\infinity e^{(-v) (+1)} dx dy\)
\(= 4\int 0\infty y [-e^{(-v) (+1)} ]0\infty dy\)
\(= 4\int0\infty y (0 - (-1)) dy\)
\(= 4\int 0\infty y dy\)
\(= 4[(y^2)/2]0\infty\)
\(= 2\infty ^2\)
\(= \infty\)
Therefore, the integral of f(x, y) over the entire plane is equal to\(\infty\) , which means that f(x, y) is not a probability density.
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Related Questions
Another enlargement of the photograph is made. The shorter side has length 7.5 cm Work out the longer side.
Answers
The length of the longer side, given the length of the shorter side, is 9. 38 cm
How to find the length ?The photograph at it's original size measures 8 cm by 10 cm. This means that the ratio of the smaller side to the larger side is :
= 8 / 10
= 80 %
If the smaller side is 80 % of the larger side, then the long side length when an enlargement of the photograph is made is :
= Length of shorter side / Ratio of shorter side
= 7. 5 / 80 %
= 9. 375 cm
= 9. 38 cm
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The first part of the question is:
A photograph measures 8cm by 10cm.
what the simplified form of 3
Answers
Answer:
It’s the last one.
Step-by-step explanation:
135 can also be written as 9 times 15. Since this is a square root, find a factor that is repeated twice. 9 can be broken down into 3 times 3. Hence this goes on the outside. 15 stays inside.
finddy/dx and d2y/dx2,and find the slope and concavity (if possible) at the given value of the parameter. (if an answer does not exist, enter dne.)parametric equations pointx = 7t, y = 5t − 1t = 9
Answers
We have the parametric equations:
x = 7t, y = 5t - 1
Differentiating each equation with respect to t, we get:
dx/dt = 7, dy/dt = 5
Using the chain rule, we have:
dy/dx = dy/dt ÷ dx/dt = 5/7
Differentiating dy/dx with respect to x, we get:
d2y/dx2 = d/dx(dy/dx) = d/dx(5/7) = 0
Therefore, the slope of the curve at any point is 5/7, and the curve has zero concavity everywhere. Since the parameter t is not specified, we cannot find the slope and concavity at a specific value.
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From the graph of the function, determine the domain and the range.
A. Domain: (–4, –2] Range: (–3, 0)
B. Domain: (–4, 4) Range: [–3, 0]
C. Domain: [–4, –2] Range: [–1, 0)
D. Domain: (–4, 3] Range: (1, 0)
![From the graph of the function, determine the domain and the range. A. Domain: (4, 2] Range: (3, 0) B.](https://i5t5.c14.e2-1.dev/c-qa-images/contents/attachments/e7HkMmqSrxVjy0BooooZRwJfOtUzJHkr.png)
Answers
Answer:
Domain(-4,4) and Range:(-3,0)
Step-by-step explanation:
Because the graph goes through - 4 and 4
You roll a die, spin the spinner, pick a card, and find the sum. How many different sums are
possible?
die: 6
spinner: 6
7
card: 6 7
Answers
There are 72 different sums that can be obtained by rolling the die, spinning the spinner, and picking a card.
To determine the number of different sums possible, we need to consider the outcomes of rolling the die, spinning the spinner, and picking a card.
Let's analyze each component separately:
1. Rolling the die: The die has 6 sides, numbered 1 to 6. Therefore, there are 6 possible outcomes when rolling the die.
2. Spinning the spinner: The spinner has 6 sections labeled 1 to 6. Again, there are 6 possible outcomes when spinning the spinner.
3. Picking a card: The card has two options, either 6 or 7. Thus, there are 2 possible outcomes when picking a card.
To find the total number of different sums, we need to multiply the number of outcomes for each component. Therefore, the total number of different sums is obtained by multiplying 6 (die outcomes) by 6 (spinner outcomes) by 2 (card outcomes), resulting in 6 * 6 * 2 = 72 different possible sums.
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Please help me I need this to be done it would mean a lot :)
Answers
Answers:
16. sin(A) = a/12
17. tan(A) = a/9
18. sin(B) = 3/4 (reduced from 9/12)
19. cos(B) = a/12
===================================================
Explanation:
The sine of an angle is equal to the ratio of the opposite side over the hypotenuse. For reference angle A, the opposite side is BC = a. The hypotenuse is always the longest side. The hypotenuse is AB = 12.
sin(angle) = opposite/hypotenuse
sin(A) = BC/AB
sin(A) = a/12
Similarly,
sin(B) = opposite/hypotenuse = AC/AB = 9/12 = 3/4.
--------------------
Tangent is the ratio of opposite over adjacent
tan(angle) = opposite/adjacent
tan(A) = BC/AC
tan(A) = a/9
--------------------
Cosine is the ratio of adjacent over hypotenuse
cos(angle) = adjacent/hypotenuse
cos(B) = BC/AB
cos(B) = a/12
we see that this is the same result as sin(A). It turns out that sin(A) = cos(B) if and only if A+B = 90. In other words, the sin(A) = cos(B) when A and B are the acute angles of a right triangle.
--------------------
Side note: you could use the Pythagorean theorem to solve for the value of 'a'. All of this assumes that triangle ACB is a right triangle.
Hailey has 48 inches of ribbon. How many feet of ribbon does she have?
Answers
Conversion:
12 inches = 1 foot
Divide:
48 / 12 = 4
Therefore, Hailey has 4 feet of ribbon.
Best of Luck!
Answer: 4 foot of ribbon
Step-by-step explanation: there is 12 inches in one foot so this means to get the answer you must divide 48 by 12 to get 4 so 4 feet is the answer
hope this helps and mark me brainliest if it did hope you have a great day
What are the solutions to the quadratic equation 4(x + 2)2 = 36
x = -11 and x = 7
x = -7 and x = 11
x = -5 and x = 1
x= -1 and x = 5
mentary
condary
s Notebo...
Spring
Previous Activity
Answers
Answer:
C) x = −5 and x = 1
Step-by-step explanation:
I took the test and I got it right
The solutions to the quadratic equation \(4(x + 2)^2 = 36\) are as x = -5 and x = 1.
What is a solution for a quadratic equation?Suppose that we've a function y = f(x) such that f(x) is quadratic.
When y = 0, then the values of x for which f(x) = 0 is called solution of quadratic equation f(x) = 0
This solution gives values of x, and when we plot x and f(x), we'd see that the graph intersects the x-axis at its solution points.
We have the given quadratic equation
\(4(x + 2)^2 = 36\)
solving for x
\(4(x + 2)^2 = 36\\\\(x + 2)^2 = 36/4\\\\(x + 2)^2 = 9\\\\(x + 2)^2 = 3^2\\\\(x + 2) = 3\\\\x = 1\\or \\\\x + 2 = -3\\\\x = -5\)
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With a partner, you are going to research recipes and find examples of fractional
amounts of spices and/or seasonings. Use cookbooks, recipe cards, or on-line sources to find recipes of your favorite foods. You
can even interview a chef or cook! Find 3 recipes that have at least one ingredient that
uses a fractional amount of some of the ingredients. Choose one of the ingredients that is a fractional amount. If you were to double
the recipe, how much of the ingredient would you use? Talk to an adult about what
operation you would use to double the amount. Practice doubling some of the fractional
amounts with the 3 recipes you chose. Create a recipe with fractional amounts of several ingredients. Then have another
student double your recipe
Answers
There are three recipes provided to mention the fractional amounts of ingredients:
Recipe for Chicken Curry:
2 teaspoons of turmeric
1/2 teaspoon of cumin
1/4 spoon of any type of pepper
If you were to double this recipe, you would use:
4 teaspoons of turmeric
1 teaspoon of cumin
1/2 teaspoon of pepper
To double the amount of the ingredients, you would multiply each fraction by 2.
Chocolate chip cookies:
1/4 teaspoon of baking soda
1/2 teaspoon of salt
double the quantities if u want to make more or huge quantities
Tomato soup recipe
half a spoonful of dried basil
1/4 teaspoon of dried thyme
for this recipe, we will need
1 spoon of basil
1/2 teaspoon of dried thyme
Recipe for Pasta Salad:
fourth cup of Olive oil
1/3 cup of red wine vinegar
1/2 teaspoon of dried oregano
1/4 teaspoon of salt
1/8 teaspoon of black pepper
We can multiply by 2 if we increase the quantity.
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Hi, may someone help me with this question? Thank you!:)
“If f(x) = x^2 + 7, find f(x+2)”
Answers
Answer:
=x^2 +4x+11
Step-by-step explanation:
f(x) = x^2 + 7,
Replace x with x+2
f(x+2) = (x+2)^2 + 7
= (x+2)(x+2) +7
FOIL
= x^2 +2x+2x+4 +7
Combine like terms
=x^2 +4x+11
Answer:
\(f(x+2)=x^2+4x+11\)
Step-by-step explanation:
In \(f(x)=x^2+7\), for all values of \(x\), we substitute \(x\) (what is in the parentheses) into \(x^2+7\) to output a \(y\) value.
In \(f(x+2)\), the term \((x+2)\) is in the parentheses. Therefore, substitute \((x+2)\) for \(x\) in \(x^2+7\) to find \(f(x+2)\):
\(f(x+2)=(x+2)^2+7\)
Expand using \((a+b)^2=a^2+2ab+b^2\),
\(f(x+2)=x^2+4x+4+7\)
Combine like terms:
\(\boxed{f(x+2)=x^2+4x+11}\)
A gardener has 1300 saplings. He wants to plant these in such a way that the number of columns and the number of rows remain same. Find the least number of more saplings he needs for this.
Answers
Answer:
69
Step-by-step explanation:
Square root of 1300= 36
(37)²>1300>(36)²
Therefore , the requirement no. to be added to get a perfect square
=(37)²=1369
= 1369- 1300=69
The least no. Of sapling he needs for this = 69
What’s the answer to this? Thanks!
Answers
Answer:
D
Step-by-step explanation:
I used a triangle calculator I'm not really sure how to calculate it by hand. if the angle of sides 4 and 15 is set to 1 then the min is 11.33 and if the andle of sides 4 and 15 are set to 179 then the max is 18.99952
Sorry if this isnt enough, but i am sure.
Answer:
D. 11 < x < 19.
Step-by-step explanation:
The third side x is between 11 and 19 cm.
Consider sides AB (length 4) and BC (length 15) of the triangle.
Consider the angle between AB and BC is slightly less than 180 degrees. To get from point A to point C, we have to travel almost the entire length of A to C, which is from A to B and then B to C, so a bit less than 19 cm.
Consider the angle between AB and BC is slightly more than 0 degrees. To get from point A to point C, we subtract the length of AB (because we're already further along BC), so 15 - 4, a bit greater than 11.
Find the 104th term of the sequence: -4, -1, 2, 5, ..
Answers
Answer:
the 104th term of the given sequence is 305.
Step-by-step explanation:
The given sequence is an arithmetic sequence with the first term (a1) equal to -4, and a common difference (d) equal to 3.
We can use the formula for the nth term of an arithmetic sequence to find the 104th term:
an = a1 + (n - 1)d
Substituting the values given:
a104 = -4 + (104 - 1) x 3
a104 = -4 + 309
a104 = 305
Therefore, the 104th term of the given sequence is 305.
Answer:
305
Step-by-step explanation:a=-4
d=5-2=3
from
tn=a+(n-1)d
t(104)=(-4)+(104-1)×3
=-4+(103×3)
=-4+309
=305
find the greatest common factor of the terms: 35a⁴b⁸, 49a²b⁵, 14ab⁴?
Answers
Answer:
7ab^4
Step-by-step explanation:
all of the coefficients have 7 as a GCF. for a and b you can only pull out as much as the lowest term.
that should be correct and hope this helps!
did we prove the conclusion true for every isosceles triangle or only for this specific isosceles triangle?
Answers
∠A = ∠C for every isosceles triangle and not only for this specific isosceles triangle.
We are given that:
AB = BC
Now, draw a angle bisector from point B to the line AC in a way that it intersects AC at D.
Now, we get that:
∠ABD = ∠CBD ( BD is the angle bisector)
BD = BD ( common line)
So, ΔABD ≅ Δ CBD ( SAS property)
So,
∠A = ∠ C ( CPCT rule)
Also, it will be true for every isosceles triangle.
Therefore, we get that, ∠A = ∠C for every isosceles triangle and not only for this specific isosceles triangle.
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Your question was incomplete. Please refer the content below:
There is an isosceles triangle with AB = BC. Prove that ∠A = ∠C.
Did we prove the conclusion true for every isosceles triangle or only for this specific isosceles triangle.
True or False? A circle could be circumscribed about the
quadrilateral below.
• A. True
• B. False
Answers
Answer:
False
Step-by-step explanation:
m∆A+m∆C=180°
110°+110°=180°
220°(/=) 180°
A circle can be circumscribed about the given quadrilateral, the answer is true.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
To circumscribe a circle about a quadrilateral means to place the quadrilateral inside the circle, such that the four vertices of the quadrilateral touches the the circumference of the circle.
Opposite angles of a circumscribed polygon are supplementary.
Therefore, a circle can be circumscribed about the given quadrilateral is true
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I have worked out trapezium's area but didn't work out triangle's. I need it fast, for tomorrow
Answers
Answer:
hope this answer helps you dear.....take care and may u have a great day ahead!
Which congruency theorem can be used to prove that △ghl ≅ △khj? sss asa sas aas
Answers
We can prove that the given triangles GHL and KHJ are congruent using the ASA theorem. So, the second option is the correct answer.
We can say any two shapes are congruent if they have the same shape and size. For this, their sides and angles need to be mirror images of each other. We have four congruency theorems at hand here. These are side-side-side(SSS), angle-side-angle(ASA), side-angle-side(SAS), and angle-angle-side(AAS).
According to the ASA congruency theorem, one side and two angles of the triangles in question need to be similar. In the given image, we can see that two of the angles i.e., HGL and HKJ are congruent while GHL and KHJ are congruent. The sides GH and KH are also congruent. This makes the two triangles △GHL ≅ △KHJ by the ASA theorem. So, the second option is the correct answer.
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A probability sampling method in which we randomly select one of the first k elements and then select every k element thereafter is stratified random sampling. b. cluster sampling. systematic sampling. d. convenience sampling.
Answers
The probability sampling method in which you randomly select one of the first k elements and then select every k element thereafter is known as c. systematic sampling. Therefore, option c. systematic sampling is correct.
Systematic sampling is a probability sampling technique where the sample is chosen by selecting every kth element from the population, where k is a constant. This method is often used when the population is large and the complete list of elements is not easily available.
Stratified random sampling is a technique where the population is divided into strata or subgroups based on certain characteristics and a random sample is chosen from each stratum.
Cluster sampling involves dividing the population into clusters or groups and then selecting a random sample of clusters. The elements within each selected cluster are then included in the sample.
Convenience sampling is a non-probability sampling method where the sample is chosen based on convenience and availability. This method is often used in situations where it is difficult or expensive to obtain a random sample.
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How many four letter code words can be formed from the letters in the word "MIRAGE" if no letter is repeated, and the second-to-last letter must be a vowel?
Answers
Answer:
180
Step-by-step explanation:
6 different letters.
we need to pick groups of 4.
no repetitions, but the sequence matters (code words), as e.g. RAGE is different to GEAR, although they contain the same letters.
so, we need basic permutations (instead of combinations) :
P(6, 4) = 6! / (6 - 4)! = 6! / 2! = 6×5×4×3 = 360
that is simply because regularly we would have 6 choices for the first letter, then 5 for the second, 4 for the third, and 2 for the fourth letter.
the second to the last letter is the second letter from the left in a 4-letter word.
so, we have 3 vowels for that second position.
normally, such a restriction would mean
6×3×4×3 = 216 possibilities.
but we have to distinguish the 2 cases that we pick a vowel for the first position - or not.
if not, we have 3 consonants for the first, 3 vowels for the second position as options.
if yes, we have 3 vowels for the first and 2 vowels for the second position.
that means we get
3×3×4×3 + 3×2×4×3 = 108 + 72 = 180
possibilities.
this makes also sense, when we simply say that this restriction eliminates half of our possible permutations (all with a consonant in the second position) : 360/2 = 180.
What number should be placed in the box to help complete the division calculation?
Answers
Answer:12
Step-by-step explanation:
choose all that are correct.
1. Random samples from the same population will vary from sample to sample.
2. as the sample size increases, the sample distribution more closely resembles the population distribution.
3. vallues of a sample statistic of different random samples of the same size from the same population will be the same
4. if a random sample is chosen from a population with a large cluster of points at the maixmum, the sample is likely to have at least one element neat the maximum
Answers
Answer:
ennenennenenenenenennnnnnnnnnnnn nn
Answer: the answer is 1, 2, and 4
Step-by-step explanation:
I know this cause my teacher told me
6. births of boys with n=8 births and p=0.512 for a boy, find p(exactly 5 boys
Answers
The probability of exactly 5 boys in 8 births with a probability of 0.512 for a boy is approximately 0.281, or 28.1%.
The probability of exactly 5 boys in 8 births can be calculated using the binomial probability formula:
P(X = k) = (n choose k) * \(p^k\) * \((1 - p)^{(n - k)\)
where X is the random variable representing the number of boys, n is the number of births, p is the probability of having a boy in a single birth, and k is the specific number of boys we want to calculate the probability for.
In this case, we want to find the probability of exactly 5 boys, so we plug in n = 8, p = 0.512, and k = 5:
P(X = 5) = \((8 choose 5) * 0.512^5 * (1 - 0.512)^{(8 - 5)\)
= 0.281
Therefore, the probability of exactly 5 boys in 8 births with a probability of 0.512 for a boy is approximately 0.281, or 28.1%.
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Complete Question:
With n=8 births and the probability of having a boy p=0.512: If the requirements for using the normal approximation for the binomial distribution are met, calculate the probability of having P(exactly 5 boys). If the requirements are not met, state "Normal approximation should not be used" O 0.61 O 0.23 O None of these O Normal approximation should not be used O 0.83 O 0.77
i need to know what x equals
Answers
Answer:
x = 13
Step-by-step explanation:
The tiny marks on all three sides means this shape is an equilateral triangle (all three sides are the same) This means that all three angles are also the same. 180° degrees in a triangle, so all three angles are 60°.
Use this info to set up an equation.
4x + 8 = 60°
Subtract 8.
4x = 5 2
Divide by 4.
x = 13
Forty three fence posts are placed one yard apart. How many yards of fence is this?
Answers
Answer:
86
Step-by-step explanation:
43 x 2=86
HEY CAN ANYONE PLS ANSWER DIS MATH PROBLEM!
Answers
A peach orchard owner wants to maximize the amount of peaches produced by his orchard.
He cannot simply plant as many trees as he can, since planting more trees will decrease the amount of fruit that each tree produces (the yield of each tree).
He has found that the per-tree yield can be described by the equation
Y = 1200 - 15 x.
Here Y is the yield per tree and x is the number of trees planted per acre.
For example, if there were 10 trees planted per acre, each tree would produce 1200 - 15 * 10 = 1050 peaches.
Find the number of trees per acre that should be planted in order to produce the maximum crop and the resulting total yield.
Number of trees per acre : trees per acre
Total yield : peaches per acre
Answers
To maximize the amount of peaches produced by the orchard, the peach orchard owner should plant a certain number of trees per acre. The per-tree yield is given by the equation Y = 1200 - 15x, where Y represents the yield per tree and x represents the number of trees planted per acre.
To find the number of trees per acre that maximizes the crop yield, we need to determine the value of x that corresponds to the vertex of the equation. The vertex of a downward-opening parabola, represented by the given equation, occurs at the x-coordinate given by x = -b / (2a).
In this case, the coefficient of x is -15 and the constant term is 0, so b = 0 and a = -15. Substituting these values into the formula, we get x = -0 / (2 * -15) = 0.
While the mathematical calculation suggests that planting zero trees per acre would maximize the yield, this result is not practical. Therefore, the closest feasible value greater than zero would be 1 tree per acre.
For 1 tree per acre, substituting x = 1 into the equation, we find that each tree would produce a yield of Y = 1200 - 15 * 1 = 1185 peaches. Consequently, the resulting total yield would be 1185 peaches per acre.
Number of trees per acre: 1 tree per acre
Total yield: 1185 peaches per acre
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Given f(x)-x-5,solvr for x when f (x)=4
Answers
Answer:
-1-x
Step-by-step explanation:
i think im not sure
The town of Knappville has a landmark, L, an amusement park, AP, a high school, HS, a city hall, CH, and a city park, P. Herberto is at the amusement park and wants to go to the city hall. Name a path he could travel
Answers
Herberto travelled through Amusement Park (AP), City Park (P), Landmark (L), High School (HS), City Hall (CH).
Herberto can take the following path to travel from the amusement park (AP) to the city hall (CH):
Amusement Park (AP) -> City Park (P) -> Landmark (L) -> High School (HS) -> City Hall (CH)
This path takes him through the city park, then to the landmark, followed by the high school, and finally to the city hall.
Please note that without a specific map or layout of Knappville, there could be multiple valid paths from the amusement park to the city hall. The path provided above is just one example.
When Herberto travels from the amusement park to the city hall, he can choose various paths depending on the specific layout of Knappville. The path mentioned earlier is just one example, but the actual paths could differ based on the town's infrastructure and the locations of the landmarks.
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(L5) Theorem 5.5B states that if the measure of one angle of a triangle is greater than the measure of another angle, then the side __________ he angle with the greater measure will be longer than the side opposite the angle with the __________ measure.
Answers
Theorem 5.5B is a helpful theorem that relates the measures of angles in a triangle to the lengths of the sides opposite those angles. Specifically, it states that if one angle in a triangle has a greater measure than another angle, then the side opposite the angle with the greater measure will be longer than the side opposite the angle with the smaller measure.
This theorem can be useful in a variety of situations, such as when solving for unknown side lengths or angles in a triangle.
To understand why this theorem works, it can be helpful to think about the relationship between the measures of angles and the lengths of sides in a triangle. For example, we know that in any triangle, the sum of the measures of the three angles is always 180 degrees. We also know that the length of one side of a triangle is related to the measures of the angles opposite that side, according to the Law of Sines or the Law of Cosines.
Using these relationships, we can see why Theorem 5.5B makes sense. If one angle in a triangle is larger than another angle, then the remaining angle must be smaller to ensure that the sum of the angles adds up to 180 degrees. This means that the side opposite the larger angle must be longer than the side opposite the smaller angle, since the length of a side is related to the measure of the angle opposite that side.
In summary, Theorem 5.5B provides a helpful way to relate the measures of angles and the lengths of sides in a triangle. By understanding this theorem, we can solve problems involving unknown side lengths or angles with greater ease and accuracy.
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