- Let X And Y Be Continuous Random Variables With The Joint Probability Density Function 12 Cy If 0 X 1 X2 Yvo Fx Y R Y 1 (53.51 KiB) Viewed 97 times
Let X and Y be continuous random variables with the joint probability density function 12.cy if 0<x<1, x2 <yvo fx,y (r,y) 0 elsewhere. Calculate 1. the probability density functions fx (I) and fy(y) of the marginals. Are X and Y independent? 2. the expectation of the random vector (X, Y); the variances Var(X) and Var(Y) of X and Y. 3. the covariance of X and Y. What is the covariance matrix of the random vector (X,Y)? 4. the coefficients Bo and B, of the regression line g(x) = Bo + BX that estimates Y such that the mean squared error E|(Y – 9(X))] is minimized, using the results from parts 2 and 3. 5. the expected value E(Z) and the variance Var(2) of the random variable 2 = 3X – 7Y + 2, using the results from parts 2 and 3.