1.7 lecture07

1.7 lecture07 - STAT 1301 Probability Statistics Lecture 7...

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1 STAT 1301 Probability & Statistics Lecture 7 21 Blackjack "21" is the fact-based story about six MIT students who were trained to become experts in card counting and subsequently took Vegas casinos for millions in winnings. Gambler’s Ruin Problem Two gamblers, A and B , bet on the outcomes of successive flip of a coin. On each flip, if the coin comes up heads, A collects $1 from B , whereas if it comes up tails, A pays $1 to B . They continue to play until one of them runs out of money. Assume that the flips are independent and each flip results in a head with probability p =1/2, what is the probability that A ends up with all the money if he starts with $5 and B starts with $10? Discrete and Continuous Random Variables
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2 Example X = The sum of two tosses of a fair six- sided die. Possible values: {2, 3, 4, …, 12}. X = the total number of coin tosses required for three individuals to obtain HHH or TTT. X is a discrete rv. Its set of possible values is infinite but countable. pmf If X is a discrete rv, the function given by p ( x ) = P ( X =x ) = P (all s S : X ( s ) = x ) for each x within the range of X is called the probability mass function (pmf) of X . If a random variable can take values x i , then the following must be true: 1 ) ( . 2 1 ) ( 0 . 1 i i x all i i x p x all for
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This note was uploaded on 05/04/2011 for the course STAT 1301 taught by Professor Smslee during the Spring '08 term at HKU.

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1.7 lecture07 - STAT 1301 Probability Statistics Lecture 7...

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