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319handout4

# 319handout4 - C Can(b be a pdf If so determine C 4 Suppose...

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Econ 319, Fall 2008 TA: Simon Kwok Handout 4 1. The inhabitants of an island tell the truth one third of the time, and lie with probability 2/3. On an occasion, after one of them made a statement, another islander stepped forward and declared the statement true. What is the probability that the °rst statement was indeed true? 2. In an o¢ ce there are 200 employees. None of the employees are married to each other. Suppose that a person is chosen at random. The probability of that person being a man and being married is 1 10 . If you know that the person is married, the probability of the person being a man is 2 9 . If you know that the person is single, the probability of the person being a man is 4 11 . (a) How many married people are in the o¢ ce? (b) How many married women are in the o¢ ce? (c) If you know that the random person chosen is a woman, what is the probability that she is single? 3. Consider the following two functions (a) f ( x ) = ° C (2 x ° x 3 ) if 0 < x < 5 2 0 otherwise, (b) f ( x ) = ° C (2 x ° x 2 ) if 0 < x < 3 2 0 otherwise. Can (a) be a probability density function (pdf)? If so, determine
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Unformatted text preview: C . Can (b) be a pdf? If so, determine C . 4. Suppose a random variable X has a cdf: F ( x ) = 8 > > > > < > > > > : x < & 2 : 4 & 2 ± x < : 5 ± x < 1 : 8 1 ± x < 4 1 x ² 4 : (a) Find the probability (mass) function f ( x ) and give your reasoning. (b) Find the values for: 1. Pr( x ± 1) ; 2. Pr( x > 1 2 ) ; 3. Pr( x = 0) : 5. (For those who are up to more challenge. Not for exam) Consider two gamblers, A and B. A has \$5 and B has \$10. They play a game in which they ±ip a fair coin. If it comes up a head then A gives B a dollar. If it comes up a tail then B gives A a dollar. They continue like this until one player has no money left²the other player is then considered to be the winner. What is the probability that A wins this game? [Hint: Let p ( i ) denote the probability that a player wins given that this payer has \$ i . Use conditional probability to show the recursion ( i + 1) p ( i ) = ip ( i + 1) by induction.] 1...
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