E (X+ Y)
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- Suppose that the random variables X and Y have a joint density function f(x,y).prove that Cov(X,Y)=0 if E(X|Y=y) does not depend on yLet X be a continuous random variable with density functionf(x) = 3x^-4, x ≥ 1. Compute E(X ) and Var(X ).Suppose a continuous random variable X~Fx(x): f(x,y) = {1/4e^-1x/4, if x≥0 0, x<0} What is the cumulative density function of Y=min{2,X}?
- Suppose that the random variables X and Y have a joint density function given by: f(x,y)={cxy for 0≤x≤2 and 0≤y≤x, 0 otherwise Find the constant c, P(Y≥1/2), P(X < 2, Y >1/2), P(X < 1), Determine whether X and Y are independent.Suppose the random variables X and Y have joint probability density function f(x,y) given by: (image)Find: P(X < Y) = fX|Y=y (x)Let X and Y be two continuous random variables with joint probability density function f(x,y) = 2xy for 0 < x < y < 1. Find the covariance between X and Y.
- Assume that X and Y are jointly continuous random variables with joint probabilitydensity function given by A. Find the marginal density functions for X and Y . B. Find E[X] and E[Y ]. C. Find Cov(X, Y ).Let X and Y be independent uniform random variables on (0, 1). Find their joint density function f (x, y). Use the joint density function to calculate the probability P(X < Y).Suppose random variable X has a density function f ( x ) = { 2 /x 2 , 1 ≤ x ≤ 2 0 , o t h e r w i s e . Then E[X4] =?
- Let X and Y be two continuous random variables with joint probability density function f(x,y) = k(x + y) for 0 < x < 1, 0 < y < 1 and 0 otherwise, where k is a constant. Find the marginal probability density functions of X and Y.Let X and Y be random variables with the joint density function f(x,y)=x+y, if x,y element of [0,1], and f(x,y)=0,elsewhere. Find the expected value of the random variable Z = 10X+14Y.Suppose that X is a continuous random variable with density function f(x). If f(x)=k for −5≤x≤3 and f(x)=0 otherwise, determine the value of k.