1. Suppose that E(X) E(Y) E(Z) 2 Y and Z are independent, Cov(X, Y) V(X) V(Z)...
3Y 2 1. (20 points) Suppose that X and Y independent random variables. Let W 2x (a) Consider the following probability distribution of a discrete random variable X: 12 P(X) 00.7 0.3 X Compute the mean and variance of X (b) Use your answers in part (a). If E(Y)=-3 and V(Y)= 1, what are E(W) and V (W)?
Assume X, Y are independent with EX = 1 EY = 2 Var(X) = 22 Var(Y) = 32 Let U = 2X + Y and V = 2X – Y. (a) Find E(U) and E(V). (b) Find Var(U) and Var(V). (c) Find Cov(U,V).
-1 1 9. Suppose the discrete random variables X and Y are jointly distributed according to the following table: 0 0.1 0.1 0.1 3 0 0.2 0.1 4 0.2 0.1 0.1 2x 1 a. Compute the expected values E(X) and E(Y), variances V(X) and V(Y), and covariance Cov(X,Y) of X and Y. [11] b. Let W = X – Y. Compute E(W) and V(W). [4]
Extra: Let X, Y, Z be results of three independent tosses of a fair die. (a) Find the covariance of the random variables W=2X-3Y + Z (b) Find the correlation coefficient of W and V. and V=X-2Y-Z
Suppose the random variables X, Y and Z are related through the model Y = 2 + 2X + Z, where Z has mean 0 and variance σ2 Z = 16 and X has variance σ2 X = 9. Assume X and Z are independent, the find the covariance of X and Y and that of Y and Z. Hint: write Cov(X, Y ) = Cov(X, 2+2X+Z) and use the propositions of covariance from slides of Chapter 4. Suppose the...
• Suppose X, and X2 are Independent random Variables with Exi) = E(X2) - 1, V(X)=1 and V(X2) 24. ca Find v(2X-X2). (b) Find CoV (X,+ X2 +2 , X, X2 ).. (c) Findcov (x1+x2 + 2 X, - X2+3). do Find v(x,x2). (e) Find cov (X1, X, X2).
Suppose that Cov(X,Y ) = 0.9 and Cov(X,Z) = −0.7. (a) What is Cov(X,Y + Z)? b) What is Cov(3X,−2Y )?
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...
Suppose XX and YY are independent random variables for which Var(X)=7Var(X)=7 and Var(Y)=7.Var(Y)=7. (a) Find Var(X−Y+1).Var(X−Y+1). (b) Find Var(2X−3Y)Var(2X−3Y) (c) Let W=2X−3Y.W=2X−3Y. Find the standard deviaton of W.W.
Please show steps (and formulas) for part b Problem 2. a. X has a normal distribution with mean 5 and variance 25. Y has a normal distribution with mean 3 and variance 16. In addition, X and Y are independent. If W = X+Y, find P(W > 9). b. Random variables U, V, Z are such that E[U] = 1, E[V] =5, E[2] = -3, Var[U] = 1, Var[V] = 4, Var[2] =1, Cov[U,V] =-1,Cov[U, 2] = 2, Cor[V, 2]...