sol06

# Monte hall has removed an incorrect option from the

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: te Hall has removed an incorrect option from the unchosen doors, so contestants who switch double their chances of winning the prize. 4. Funds A, B, and C can each make \$1 or lose \$1 with 50% probability. Assume the funds are pairwise symmetric: for any pair of funs i and j, (= 1&= 1) = (= -1&= -1) (= 1&= -1) = (= -1&= 1) The correlation between A and B is , and the correlation between B and C is also . How high does need to be so that the correlation between A and C is necessarily positive? Solution: Let ( ) ( ) ( ) ( ) Then we have: We know: Hence, ( ) ( ) ( ( (( (( (( Hence, ( Similarly, since ( ( ( ) ( ( ( ( ) ) ( )( )( ) )( )( ) )( )( ) )( )( ) ( ) ( )) ) ) )( )( ( ) ) ) ) )( )( ( )( )( ) (( ) ) )( )( ) ( ) ( ) ( ) ) ) ( ( ( ) ) ) ( ) ( ( Therefore, we need ( ) ( Note: if we have two variables: A and B, which could be 0 or 1. Then, A=1 has two possibilities: 1. A=1 and B=1 2. A=1 and B=-1 ( ) ( Hence, ( ) Therefore, ( ) ( ( ( Remember that ( ( Therefore, ( ) ( ( ) ( ) ) ) ( ) ( ) ) ) ) ) ( ) ) ) ( ( ) ( ) ( ) i.e., we need:...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online