07_Discrete Probability Distributions Part 1

# What is the probability a person in the study

• Notes
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What is the probability a person in the study preferred a sports drink? 7 P(B) = 280 400 = 0.7 P(S) = 1 - P(B) =1- 0.7 = 0.3

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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(M|S) = 80 120 = 0.667 P(W |S) = 40 120 = 0.333 P(M S ) = P(M|S) P(S) = 0.667* 0.3 = 0.2 P(W S ) = P(W |S) 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(S|M) = P(S M ) P(M) = 0.2 0.5 = 0.4 P(S| W) = P(S W ) P(W) = 0.1 0.5 = 0.2

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Example Is preference for a sports drink independent of whether the consumer is a man or a woman? Not independent! 10 P(S|M) = 0.4 P(S) = 0.3 P(S|M) 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

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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

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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 real-number 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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