6. Two independent random variables X1=(-1,0,1) and X2=(-1.0) can take the following probability values: P(X1-1)-p, P(X1=0)=2p, P(X1=1)=1-3p, P(X2=-1)=p, P(X2=0)=1-p. Si X=X1+X2 y Y=X1*X2, determine E(XY).
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- 4. Show that if X and Y are independent random variables, then E(g(X)| X = ro) = 9(ro).If X and Y are independent random variables with E(X) = 10, Var(X) = 4, E(Y) = 12 and VAR(Y) = 3, If W =-2X +Y Find E(W) and STD (W) (a) (b) If X and Y are not independent, with E(X) =10, VAR(X) = 5, E(I) =18, VAR(Y) = 3 and CovX,Y) = -2. If W = X – 2Y Find E(W) and STD(W)For a random variable X, suppose that E[X] = 1 and Var(X) = 5. Then %3D (a) E[(2 + X)²] = (b) Var(2 + 3X) = Netsu rtiol orodit on this problem
- A4. If random variables X and Y each have variance o? = 3 and corr(X,Y) = 0.4, what is the value of Cov(3X – 1, 2Y + 2)?5. Show that given random variables X and Y, Cov(X, E(Y | X)) = Cov(X, Y). %3DIf the joint probability distribution of X and Y isgiven byf(x, y) = 130 (x + y) for x = 0, 1, 2, 3; y = 0, 1, 2 construct a table showing the values of the joint distribu-tion function of the two random variables at the 12 points (0, 0),(0, 1), ... ,(3, 2).
- 9. Given that f(x, y) = (2x+2y)/2k if x = 0,1 and y = 1,4, is a joint probability distribution function for the random variables X and Y. Find: (f(x|y = 1)25. Suppose X is a random variable distributed with mean u and standard deviation a > 0. If the random variable Y is defined as Y = u(X - uX)/a, then E(Y) is: a. 0 b. 1 d. E(X)Suppose Y is a random variable with E(Y) = 13 and Var(Y) = 6. Solve for the following: (show complete solution) a. E(3Y+ 10) = ? b. E(Y^2) = ? c. Var (10) = ? d. Var (5) = ?
- 10. Two random variables X and Y take on the values i and 2 with probability 1/2' (i = 1,2, ...). Show that the probabilities sum to one. Find the expected value of X and Y.2. The discrete random variable X has the probability function kx, P(X = x) = }k(x – 2), 0, x = 2,4,6 x = 8 otherwise Where k is a constant. (a) Show that k %3D 18 (b) Find the exact value of F(5).a.2 b.-1 c.0 d.-2 e.1