hw2 - Assignment #2 Reading: Sections 2.2 2.3, 3.1 3.3...

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Unformatted text preview: Assignment #2 Reading: Sections 2.2 2.3, 3.1 3.3 Chapter 2: 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 24, 25, 26, 27, 28, 30(a,b,c), 31, 32, 33, 38, 40 Chapter 3: 1, 2, 3, 4, 5, 6, 7, 8, 11(a), 12, 13, 15, 17, 19, 20 21, 22, 23, 24(a), 25, 26, 27 C Exercises: C- 1 through C7 (see below) Exercises C Here are a few more exercises which use lecture material related to Chapters 2 and 3. Problem- 1. Two gamblers ( A and B ) play the following game. To start off, each of them puts one dollar in the pot. One of these dollars is marked with an X. Then the players alternate taking turns starting with A (that is, A , B , A , B , . ..). Each turn consists of the following: a player reaches into the pot and pulls out a dollar at random. If it is the marked dollar, the player wins all the money in the pot and the game is over. If it is not the marked dollar, the player puts it back into the pot, and then adds one more dollar to the pot and the game continues. Let Y denote the total length of the game, that is, the total number of draws from the pot. Let Z be the winnings of player A . (Note that Z is negative if B wins.) Find EY and EZ . Problem 0. Use indicator random variables to prove the principle of inclusion-exclusion for the case of 3 events. (The proof works for any number of events, but the notation becomes more complicated.) Hint: Start by using DeMorgans Law ( A B C ) c = A c B c C...
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hw2 - Assignment #2 Reading: Sections 2.2 2.3, 3.1 3.3...

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