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Let X have a uniform distribution on the interval (0,1) a. Find the probability distribution of Y...
5. Let X have a uniform distribution on the interval (0,1). Given X = x, let...
5. Let X have a uniform distribution on the interval (0,1). Given X = x, let Y have a uniform distribution on (0, 2). (a) The conditional pdf of Y, given that X = x, is fyıx(ylx) = 1 for 0 < y < x, since Y|X ~U(0, X). Show that the mean of this (conditional) distribution is E(Y|X) = , and hence, show that Ex{E(Y|X)} = i. (Hint: what is the mean of ?) (b) Noting that fr\x(y|x) =...
Let the joint probability density function for (X, Y) be f(x,y) s+y), x>0, y>0, 7r+yCT, 0...
Let the joint probability density function for (X, Y) be f(x,y) s+y), x>0, y>0, 7r+yCT, 0 otherwise. a. Find the probability P(X< Y). Give your answer to 4 decimal places. 28 Submit Answer Tries 0/5 b. Find the marginal probability density function of X, fx(x). Enter a formula in the first box, and a number for the second and the third box corresponding to the range of x. Use * for multiplication, / for division and л for power. For...
a. Let X ~ Uniform(0,1). Find the distribution function of Y =-21nX. What is the distribution...
a. Let X ~ Uniform(0,1). Find the distribution function of Y =-21nX. What is the distribution of Y. Find P(Y> 0.01)
Let X be a random variable with probability density function fx(2, -1 9. f(y) y> 9. Submit Answe...
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Let X be a random variable with probability density function fx(2, -1 <z<3, 0 otherwise. Find the probability distribution of Y-X2 for 0 < y < 1, 1 < y < 9, and y > 9. [Obviously, fy(y)-0 for y < 0.1 Case 1: O < y < 1. Enter a formula below. Use * for multiplication, / for divison, ^ for power and sqrt for square root. For example, sqrt y...
The numbers x, y, z are independent with uniform distribution on [0,1]. Find the probability that...
The numbers x, y, z are independent with uniform distribution on [0,1]. Find the probability that one can construct a triangle with sides length x, y, z.
12. Let X and Y be independent random variables, where X has a uniform distribution on the interval (0,1/2), and Y...
12. Let X and Y be independent random variables, where X has a uniform distribution on the interval (0,1/2), and Y has an exponential distribution with parameter A= 1. (Remember to justify all of your answers.) (a) What is the joint distribution of X and Y? (b) What is P{(X > 0.25) U (Y> 0.25)}? nd (c) What is the conditional distribution of X, given that Y =3? ur worl mple with oumbers vour nal to complet the ovaluato all...
Let the random variable X have a uniform distribution on [0,1] and the random variable Y...
Let the random variable X have a uniform distribution on [0,1] and the random variable Y (independent of X) have a uniform distribution on [0,2]. Find P[XY<1].
U is Uniform distribution here Let X ~ U[0,1] and Y = max {,x) (a) Is...
U is Uniform distribution here
Let X ~ U[0,1] and Y = max {,x) (a) Is Y a continuous random variable? Justify (b) Compute E[Y]. (Hint: Note that when a (Hint: Note that when a-, max 1.a- , and when a > ļ, max | , a- ax {3a, and when a > a
Let X and Y be continuous and independent random variables, both with uniform distribution (0,1). Find the functions of probability densities of (a) X + Y (b) X-Y (c) | X-Y |
Let X and Y be continuous and independent random variables, both with uniform distribution (0,1). Find the functions of probability densities of (a) X + Y (b) X-Y (c) | X-Y |
Let Z ~ N(0,1) and let Y = Z2. Find the distribution of Y. Hint: Use...
Let Z ~ N(0,1) and let Y = Z2. Find the distribution of Y. Hint: Use moment generating function. Let X ~ N(j = 1, 02 = 4). If Y = 0.5*, find E(Y?). Hint: Use moment generating function.
5. Let X have a uniform distribution on the interval (0,1). Given X = x, let Y have a uniform distribution on (0, 2). (a) The conditional pdf of Y, given that X = x, is fyıx(ylx) = 1 for 0 < y < x, since Y|X ~U(0, X). Show that the mean of this (conditional) distribution is E(Y|X) = , and hence, show that Ex{E(Y|X)} = i. (Hint: what is the mean of ?) (b) Noting that fr\x(y|x) =...
Let the joint probability density function for (X, Y) be f(x,y) s+y), x>0, y>0, 7r+yCT, 0 otherwise. a. Find the probability P(X< Y). Give your answer to 4 decimal places. 28 Submit Answer Tries 0/5 b. Find the marginal probability density function of X, fx(x). Enter a formula in the first box, and a number for the second and the third box corresponding to the range of x. Use * for multiplication, / for division and л for power. For...
a. Let X ~ Uniform(0,1). Find the distribution function of Y =-21nX. What is the distribution of Y. Find P(Y> 0.01)
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Let X be a random variable with probability density function fx(2, -1 <z<3, 0 otherwise. Find the probability distribution of Y-X2 for 0 < y < 1, 1 < y < 9, and y > 9. [Obviously, fy(y)-0 for y < 0.1 Case 1: O < y < 1. Enter a formula below. Use * for multiplication, / for divison, ^ for power and sqrt for square root. For example, sqrt y...
12. Let X and Y be independent random variables, where X has a uniform distribution on the interval (0,1/2), and Y has an exponential distribution with parameter A= 1. (Remember to justify all of your answers.) (a) What is the joint distribution of X and Y? (b) What is P{(X > 0.25) U (Y> 0.25)}? nd (c) What is the conditional distribution of X, given that Y =3? ur worl mple with oumbers vour nal to complet the ovaluato all...
U is Uniform distribution here
Let X ~ U[0,1] and Y = max {,x) (a) Is Y a continuous random variable? Justify (b) Compute E[Y]. (Hint: Note that when a (Hint: Note that when a-, max 1.a- , and when a > ļ, max | , a- ax {3a, and when a > a
Let Z ~ N(0,1) and let Y = Z2. Find the distribution of Y. Hint: Use moment generating function. Let X ~ N(j = 1, 02 = 4). If Y = 0.5*, find E(Y?). Hint: Use moment generating function.
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