1. Consider the following distribution of (X,Y) where X and Y are both binary random variables:...
1. Consider the following distribution of (X,Y) where X and Y are both binary random variables: 1/4 if (, y) (0,0) 1/8 if(x, y) = (1,0) 3/8 if (, y) (0,1) y(2, y) = 1/4 if(x, y) = (1,1). (f) What is the covariance between Y and Xi
1. Consider the following distribution of (X Y) where X and Y ae both binary random variables: 1/4 i (a)-(0.0 1/4 if (x, y) (0,0) 1/8 if (r,y) (1,0) Jx3/8 if (r,)- (0,1) ,Y (z, y) = 1/4 if (, ) (11 (a) What is the probability density function of Y? (b) What is the expectation of Y1 (c) What is the variance of Y? (d) What is the standard deviation of Y? (e) Do the same to X. (f)...
1. Assume that X and Y are both binary random variables. Assume that there are constants, Bo and B such that Y-Ao + AX + t. Assume Elu 1 X-0. (a) Express EY | X-0nters of Bo and B1. (b) Express EY | X = 1] in terms of A, and A. (c)Assume that the joint pdf for (X, Y) is 1/4 f(,y) (0,0) 1/8 if(x, y) = (1,0) 3/8 if (r, y) (0,1) 1/4 if (x,y) - (1, 1)....
1. Let X and Y have a discrete joint distribution with ( P(X = x, Y = y) = {1, 10, if (x, y) = (-1,1) if x = y = 0 elsewhere Show that X and Y are uncorrelated but not independent. [5 points] 2. Let X and Y have a discrete joint distribution with f(-1,0) = 0, f(-1,1) = 1/4, f(0,0) = 1/6, f(0, 1) = 0, $(1,0) = 1/12, f(1,1) = 1/2. Show that (a) the two...
14. Random variables X and Y have a density function f(x, y). Find the indicated expected value. f(x, y) = (xy + y2) 0<x< 1,0 <y<1 0 Elsewhere {$(wyty E(x2y) = 15. The means, standard deviations, and covariance for random variables X, Y. and Z are given below. LIX = 3. HY = 5. Az = 7 Ox= 1, = 3, oz = 4 cov(X,Y) = 1, cov (X, Z) = 3, and cov (Y,Z) = -3 T = X-2...
Let X and Y be two discrete random independent random variables. p(x) = 1/3 for x =-2,-1,0 p(y) = 1/2 for y =1,6 Z = X + Y. What is the distribution of Z using the method of MGF's
Suppose X, Y are random variables whose joint PDF is given by . 1 0 < y < 1,0 < x < y y otherwise 0, 1. Find the covariance of X and Y. 2. Compute Var(X) and Var(Y). 3. Calculate p(X,Y).
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...
Consider the following joint probability distribution on the random variables X and Y given in matrix form by Pxy P11 P12 P13 PXY-IP21 p22 p23 P31 P32 P33 P41 P42 P43 HereP(i, j) P(X = z n Y-J)-Pu represents the probability that X-1 and Y = j So for example, in the previous problem, X and Y represented the random variables for the color ([Black, Red]) and utensil type (Pencil,Pe pblackpen P(X = Black Y = Pen) = P(Black n...
Suppose X, Y are random variables whose joint PDF is given by fxy(x,y) = { 0<y<1,0<=<y 0, otherwise 1. Find the covariance of X and Y. 2. Compute Var(X) and Var(Y). 3. Calculate p(X,Y)