{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

test567-10

# test567-10 - A-AE 567 Quiz Spring 2010 Clearly write your...

This preview shows pages 1–6. Sign up to view the full content.

A-AE 567 Quiz Spring 2010 Clearly write your final answer on the exam. NAME: 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Problem 1. Assume that x is uniform over { x : 1 ≤ | x | ≤ 2 } , that is, f x ( x ) = γ if 1 ≤ | x | ≤ 2 = 0 otherwise . Let y = x 2 . Compute E y = Find the density f y ( y ) = 2
Problem 2. Assume that y = x + v where x and v are two independent random variables. The random variable v is uniform over [ - 1 , 1] while the random variable x is uniform over { x : 1 ≤ | x | ≤ 2 } , that is, f x ( x ) = γ if 1 ≤ | x | ≤ 2 = 0 otherwise . Let H = span { 1 , y } . Then compute (i) b x = P H x = (2) E ( x - b x ) 2 = 3

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Problem 3. Consider the joint density for x and y given by f xy ( x, y ) = γe - ( x y ) if 0 x ≤ ∞ and 0 y 1 = 0 otherwise (i) Compute the constant γ = (ii) E ( x | y = y ) = b g ( y ) = 4
Problem 4. Consider the vectors in C 3 given by φ 1 = 1 1 1 φ 2 = 0 1 - 1 x = - 1 2 1 . Let H = span { φ 1 , φ 2 } . Then compute the orthogonal projection b x = P H x = αφ 1 + βφ 2 where α and β are constants. Recall that the inner product on C 3 is given by ( y, z ) = y 1 z 1 + y 2 z 2 + y 3 z 3 where y =

This preview has intentionally blurred sections. Sign up to view the full version.

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

{[ snackBarMessage ]}

### Page1 / 6

test567-10 - A-AE 567 Quiz Spring 2010 Clearly write your...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online