HW1 - 3 Evaluate the following equation(a ⎟ ⎟ ⎠ ⎞...

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1036: Probability & Statistics HW#1 1. Adam and Andrew toss a fair coin n +1 times. What is the probability that Adam gets more heads than Andrew? 2. Two gamblers play the game of “heads and tails”, in which each time a fair coin lands heads up, player A wins $1 from B, and each time it lands tails up, player B wins $1 from A. Suppose that player A initially has a dollars and player B has b dollars. If the game is not fair and on each play, gambler A wins $1 form B with probability p , 0< p <1, p 1/2, and loses $1 to B with probability q =1- p . If the game plays successively, what is the probability that A will be ruined?
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Unformatted text preview: 3. Evaluate the following equation (a) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ n n n n n " 2 1 (b) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ n n n n n n " 3 3 2 2 1 4. Text book: page 20, #7 5. Text book: page 31, #19, 20 6. Text book: page 38, #14, 16, 28 7. Text book: page 46, #9, 15 8. Text book: page 54, #5, 10, 23 9. Text book: page 60, #6 10. Text book: page 61, #7, 15...
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