Problem 1 (11 pts] The independent r.v.'s X and Y have p.d.f. f(t) = et, t>0....
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.
Suppose F(t) /6 for 0 < t < 6 is the c.df. Y. If Y is a continuous-type r.v., give the p.d.f. of Y. If Y is a discrete-type r.v., give the p.m.f. of Y. Otherwise, say that Y is none of the above. of a randorm variable
Problem 4: Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y: xe-(+) ;x>0;y>0 0 ; elsewhere fx y(x,y)- (a) Explain whether the lifetimes of two components are independent based on probability. (b) Compute the probability that the lifetime (X) exceeds 3.5 (c) Compute the probability that the lifetime of at least one component exceeds 3.5. (d) Compute the marginal pdf of X Problem 4: Two components of a minicomputer have the following...
Problem 4: Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y: xe-(+) ;x>0;y>0 0 ; elsewhere fx y(x,y)- (a) Explain whether the lifetimes of two components are independent based on probability. (b) Compute the probability that the lifetime (X) exceeds 3.5 (c) Compute the probability that the lifetime of at least one component exceeds 3.5. (d) Compute the marginal pdf of X Problem 4: Two components of a minicomputer have the following...
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).
2. Let X and Y have joint density f(x.v) = \ şcy? if 0 <x< 1 and 1 <y<2, otherwise. (a) Compute the marginal probability density function of Y. If it's equal to 0 outside of some range, be sure to make this clear. (b) Set up but do not compute an integral to find P(Y < 2X).
5. Let X be uniformly distributed in [0, 1]. Given X = x, the r.v. Y is uniformly distributed in 0, x for 0<x<1 (a) Specify the joint pdf fxy(x,y) and sketch its region of support Ω XY. (b) Determine fxly(x1025). (c) Determine the probability P(X〈2Y). (d) Determine the probability P(X +Y 1)
1. given the joint p.d.f f (x,y)= 2, 0 <x <y <1. 2. show that fx (x)=2(1- x), 0 <x <1 and fy (y)=2y, 0 <y <1 3. show that p(3/4<y<7/8 I x=1/4)=1/6
1. Let the joint p.d.f of X and Y be 2xe if 0 < x < 1 and y > x2 fxy(z, y) 0, otherwise. (a) Find the marginal p.d.f.'s of X and Y, respectively (b) Compute P(Y < 2X2) 1. Let the joint p.d.f of X and Y be 2xe if 0
6-x-4, 0x<2 0 1 2cych Exri If for two R.V. s X&Y the joint pdf is given by, otherwise Find Frix (o (1), Frix (alt), Ely/x-1]. var [Ylx-i] = E[^\x-]- (E[1\x=1])!