quiz3w96

# V in a b has mean a b2 hence for y u 1 3 we have that

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: nt, we have that E X Y = E X E Y . Since X is an exponential r.v. with parameter  = 1, its mean is E X = 1= = 1. 3 A uniform r.v. in a; b has mean a + b=2; hence for Y  U 1; 3 , we have that E Y = 2. 3 Therefore, the correlation between X and Y is E X Y = 1  2 = 2 2 e Due to the independence between X and Y , we have that Z31 E X=Y = E X E 1=Y = 1  y 1 dy = 1 lnyj3=1 = ln3=2 = 0.5493 y 2 2 1 5 Note: it is wrong to write E X=Y = E X =E Y = 1=2. f First, we need to nd out f xjy. Since X and Y are independent, we have that f xjy = fX x, 8y. Hence, to maximize f xjy over all x, we only need to maximize fX x = e,x over x  0. Obviously, the maximum is achieved at x = 0 . Hence, the best estimate of X is x = 0. Note that due to the independence, the best estimate of X is una ected what value of Y is observed. 5 3...
View Full Document

## This note was uploaded on 03/10/2013 for the course ECE 3075 taught by Professor Staff during the Fall '08 term at Georgia Tech.

Ask a homework question - tutors are online