According to HOMEWORKLIB POLICY we are instructed to answer the first 4 sub-parts of a question.
Problem 3 Let A be a "random point" that coincides with the point a1,a2,as or as...
(1 point) 3. Let X and Y be random variables with a joint probability density function f(z, y)e (a)Find the marginal distribution functions of X and Y, respectively. i.e. Find f(z) and f(y) f(x)- elsewhere (b) Identify the distribution of Y. What is the E(Y) and SD(Y) E(Y)- (c) Are X and Y independent random variables? Show why, or why not (d) Find P(1 X 2|Y 1) E SD(Y)-
Let the frequency function of the joint distribution of the random variables X and Y P(X = 2, Y = 3) = P(X = 1, Y = 2) = P(X = -1, Y = 1) = P(X = 0, Y = -1) = P(X = -1, Y = -2) = 3 a) Determine the marginal distributions of the random variables X and Y. b) Determine Cov(X,Y) and Corr(X,Y). c) Determine the conditional distributions of the random variable Y as a...
3. In this question, you will identify the distribution of the sum of independent random variables. I expect you will find that the mgf approach is your friend. (a) Let X and Y be independent Poisson random variables with means A1 and 12, respectively, and let S = X+Y. What is the distribution of S? (b) Let X and Y be independent normal random variables with means Husky and variances 07. 07. respectively, and let S = X+Y. What is...
Let the random variable X and Y have the joint probability density function. fxy(x,y) lo, 3. Let the random variables X and Y have the joint probability density function fxy(x, y) = 0<y<1, 0<x<y otherwise (a) Compute the joint expectation E(XY). (b) Compute the marginal expectations E(X) and E(Y). (c) Compute the covariance Cov(X,Y).
Problem 1. Let X be a normal random variable with mean 0 and variance 1 and let Y be uniform(0.1) with X and Y being independent. Let U-X + Y and V = X-Y. For this problem recall the density for a normal random variable is 2πσ2 (a) Find the joint distribution of U and V (b) Find the marginal distributions of U and V (c) Find Cov(U, V).
The random variables X and Y are independent with exponential densities fx (x) = e-"u(x) (a) Let Z = 2X + and w =-. Find the joint density of random variables Z and W (b) Find the density of random variable W (c) Find the density of random variable Z The random variables X and Y are independent with exponential densities fx (x) = e-"u(x) (a) Let Z = 2X + and w =-. Find the joint density of random...
Let X be a uniform(0, 1) random variable and let Y be uniform(1,2) with X and Y being independent. Let U = X/Y and V = X. (a) Find the joint distribution of U and V . (b) Find the marginal distributions of U.
3. Suppose that Yi and 2 are continuous random variables with joint pdf given by and zero otherwise, for some constant c >。 (a) Find the value of c. (b) Are Yi and Y2 independent ? Justify your answer. (c) Let Y = Yi + ½. compute the probability P(Y 3). (d) Let U and V be independent continuous random variables having the same (marginal) distri- 3 MARKS 1 MARK 3 MARKS bution as Y2. Identify the distribution of random...
3. Let the random variables X and Y have the joint probability density function 0 y 1, 0 x < y fxy(x, y)y otherwise (a) Compute the joint expectation E(XY) (b) Compute the marginal expectations E(X) and E (Y) (c) Compute the covariance Cov(X, Y)
3. Let the random variables X and Y have the joint probability density function fxr (x, y) = 0 <y<1, 0<xsy otherwise (a) Compute the joint expectation E(XY). (b) Compute the marginal expectations E(X) and E(Y). (c) Compute the covariance Cov(X,Y).