20082ee131A_1_HW4_new

# 20082ee131A_1_HW4_new - EE 131A Homework #4 Spring 2008 Due...

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Unformatted text preview: EE 131A Homework #4 Spring 2008 Due Apr. 28th K. Yao Read Leon-Garcia (3rd edition), pp. 96-104; 141-153 1. Let A and B be two mutually exclusive events. Show they are independent if and only if one or the other or both events have probability 0. (Hint: To proof C if and only if D, means that we need to show that if C is true, then D is true, as well as to show if D is true, then C is true.) 2. A coin is provided that may be biased; the probability p that it comes up heads maybe any of the nine multiples of 0.1 from 0.1 to 0.9, all nine possibilities having the same prior probability 1 9 . We can imagine the coin to have been drawn at random from a large heap of coins of nine types, indistinguishable to the eye and present in equal proportions. When a coin of type k is tossed, it comes up heads with proba- bility k = 0 . 1 k, k = 1 , 2 ,..., 9 . The selected coin is tossed twenty-five times, and seven times it shows heads, eighteen times tails. Which is the most likely of the nine possible values of...
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## 20082ee131A_1_HW4_new - EE 131A Homework #4 Spring 2008 Due...

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