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Unformatted text preview: 7 P(B) = 280 400 = 0.7 P(S) = 1 P(B)=1 0.7 = 0.3 Example What are the conditional probabilities P(M  S) and P(W  S)? What are the joint probabilities P(M ∩ S) and P(W ∩ S)? 8 P(MS) = 80 120 = 0.667 P(WS) = 40 120 = 0.333 P(M ∩ S ) = P(MS) P(S)=0.667*0.3=0.2 P(W ∩ S ) = P(WS) P(S)=0.333*0.3=0.1 Example Given a consumer is a man, what is the probability he will prefer a sports drink? Given a consumer is a woman, what is the probability she will prefer a sports drink? 9 P(SM) = P(S ∩ M ) P(M) = 0.2 0.5 = 0.4 P(SW) = P(S ∩ W ) P(W) = 0.1 0.5 = 0.2 Example Is preference for a sports drink independent of whether the consumer is a man or a woman? Not independent! 10 P(SM) = 0.4 P(S)=0.3 P(SM) ≠ P(S) 11 Random Variable Random variable Maps each outcome in a sample space to a number Discrete Random Variables Continuous Random Variables Random Variables Discrete Random Variable Continuous Random Variable Ch. 5 Ch. 6 12 Random Variable Examples: Random experiment: Toss coin 10 times and count how many heads turn up Random variable: # of times heads turns up {0,1,2,3,4,5,6,7,8,9,10} Random experiment: Observe daily price of Google stock for a month, e.g., January 2013. Random variable: Number of days it exceeds 725.00 {0,1,2,3,…,31} Random experiment: Observe sales of Amazon.com for the second quarter Random variable: Revenue during the quarter [0, $20 billion] 13 Discrete vs Continuous Random Variables When there are finitely many or countable number of values of a random variable, it is called a discrete random variable . Examples: Discrete RV? Number of spots on a die Number of items purchased by a customer Number of times you pushed snooze on your alarm this morning Outside temperature on February 1st 14 Discrete vs Continuous Random Variables When there are finitely many or countable number of values of a random variable, it is called a discrete random variable . Examples: Discrete RV? Number of spots on a die Number of items purchased by a customer Number of times you pushed snooze on your alarm this morning Outside temperature on February 1st When a random variable can take any realnumber value (in an open or closed range), it is called a continuous random variable....
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 Fall '12
 StephenD.Joyce
 Probability theory, discrete random variable

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