319handout4 - C . Can (b) be a pdf? If so, determine C . 4....

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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 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 &gt; &gt; &gt; &gt; &lt; &gt; &gt; &gt; &gt; : x &lt; &amp; 2 : 4 &amp; 2 x &lt; : 5 x &lt; 1 : 8 1 x &lt; 4 1 x 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 &gt; 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 leftthe 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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