100AHW2S - STAT 100A HWII Solution Problem 1: If we flip a...

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

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

Unformatted text preview: STAT 100A HWII Solution Problem 1: If we flip a fair coin n times independently, what is the probability that we observe k heads? k = 0 , 1 ,...,n . Please explain your answer. A: The probability is ( n k ) / 2 n . The reason is that all the 2 n sequences are equally likely, and the number of sequences with exactly k heads is ( n k ) , i.e., among the n flips, we choose k flips to be heads, and the rest of the n- k flips to be tails. The number of such choices is ( n k ) . Problem 2: Prove the following two identities: (1) P ( A | B ) = 1- P ( A | B ). A: P ( A | B ) = P ( A B ) P ( B ) = P ( B )- P ( A B ) P ( B ) = 1- P ( A | B ) . (2) P ( A B | C ) = P ( A | C ) + P ( B | C )- P ( A B | C ). A: P ( A B | C ) = P (( A B ) C ) P ( C ) = P (( A C ) ( B C )) P ( C ) = P ( A C ) + P ( B C )- P (( A C ) ( B C )) P ( C ) = P ( A | C ) + P ( B | C )- P ( A B | C ) Problem 3: Independence. If P ( A | B ) = P ( A ), prove...
View Full Document

This note was uploaded on 12/16/2008 for the course STATS 100A taught by Professor Wu during the Fall '07 term at UCLA.

Ask a homework question - tutors are online