This preview shows page 1. Sign up to view the full content.
Unformatted text preview: X N ( , 2 ) where beta(2 , 2). Compute E [ X ] and var( X ). 3 (8+8+8+8+8+8=48 points) Suppose ( X, Y ) had the following joint pdf f ( x, y ) = cxy, x 1 , y 1 , else (a) Find c . (b) Compute the marginal distributions for X and Y . (c) Are X and Y independent? (d) Compute cor( X, Y ). (e) Compute the conditional distribution of X  Y . (f) Compute E[ X  Y ]. 4 (10+10=20 points) Each of ve balls are placed in one of four boxes. A ball is placed in box A with probability .1, it is placed in box B with probability .2, it is placed in box C with probability .3, and it is placed in box D with probability .4. Compute the following probabilities. (a) Three balls are placed in box A and two balls are placed in box D. (b) Each box has at least one ball in it....
View
Full
Document
 Fall '08
 Staff
 Probability

Click to edit the document details