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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 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 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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