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Find Var(2X-Y) Two random variables X and Y are i.i.d. and their common p.d.f. is given...
7. The joint pdf of two random variables X and Y is given by 0sxs3,0s y<5 fx(x,y) 15' 0, otherwise Find Cov(X,y)
QUESTION 12 Let the random variable X and Y have the joint p.d.f. f(x,y) =(zy for 0< <2, 0 < y <2, and z<y otherwise Find P(0KY <1) 16 QUESTION 13 R eter to question 12. Find P(o < x <3I Y-1).
Problem 42.5 Let X and Y be two independent and identically distributed random variables with common density function f(x) 2x 0〈x〈1 0 otherwise Find the probability density function of X Y. 42.5 If 0 < a < l then ÍxHY(a) 2a3. If 1 < a < 2 then ÍxHY(a) -릎a3 + 4a-3. If a 〉 2 then fx+y(a) 0 and 0 otherwise.
Let X. Y be two random variables with joint density fx.x(x,y) = 2(x + y), 0<x<y<1 = 0, OTHERWISE a) Find the density of Z = X-Y b) Find the conditional density of fXlY (x|y) c)Find E[X|Y (x|y)] d) Calculate Cov(X, Z)
2. (10 pts The random variables X and Y have joint density function f(x, y) == 22 + y2 <1. Compute the joint density function of R= x2 + y2 and = tan-1(Y/X).
Part A. Let X and Y be two i.i.d. random variables that are exponentially distributed with 0.5e-x/2 an x>0 0 otherwise 6. Given W- X+Y. Find the MGF of W -23 a. e2sx b. e C. d. 7. Given W-X +Y. Find Ew] a. 4 b. 8 c. 12 d. 16 e. 24
3. (16 points) Suppose that X and Y have the following joint p.d.f. f(x,y) = for 0 < x < y,0 < y <, y 0 otherwise. Compute E[X2]y], the expectation of the conditional distribution of x2 given Y = y.
Below is the p.d.f for the random variables X and Y, f(x,y)-36 0 otherwise Find the following probability Pr(x> 2) O 7/9 2/3 O 8/9
8), Let X and Y be continuous random variables with joint density function f(x,y)-4xy for 0 < x < y < 1 Otherwise What is the joint density of U and V Y
1. Suppose that the p.d.f. of a random variable X is as follows: for 0<x<2, for 0 〈 x 〈 2. r for 0<< f(x) = 0 otherwise. Let Y - X (2 - X). First determine the c.d.f. of Y, then find its p.d.f. (Hint: when computing c.d.f., plotting the function Y- X(2 - X) which may help. )