{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Midterm-1-win06

# Midterm-1-win06 - Midterm 1 Winter 06 Moulinath Banerjee...

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

Midterm 1, Winter 06 Moulinath Banerjee University of Michigan February 22, 2006 Announcement: The exam carries 30 points but the maximum you can score is 25. (1) If X and Y are two uncorrelated random variables, are they necessarily independent? On the other hand, if they are independent, are they necessarily uncorrelated? Justify your answers. (6) (2) Let X and Y be independent standard normal random variables. Set U = (3 X + 4 Y ) / 5 and V = (4 X - 3 Y ) / 5. (i) Find the joint density of ( U, V ) and also the marginal densities. (8) (ii) Show that U 2 + V 2 is distributed like an exponential random variable with parameter 1 / 2. (4) (3) Two helicopters land independently of each other on the plane.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Ask a homework question - tutors are online