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Unformatted text preview: Discrete Sample Spaces If a sample space contains a finite number of outcomes, or a countably infinite collection of outcomes, it is called a discrete sample space and X is called a discrete random variable . Problem: A basketball player consistently makes 70% of her free throws. In practice one day, she is told to shoot free throws until she makes a basket. The random variable, X , counts the number of shots she takes before she can stop. Probability distribution for this free throw problem: x P(X = x) 1 0.70000 2 0.21000 3 0.06300 4 0.01890 5 0.00567 6 0.00170 7 0.00051 8 0.00015 x P(X = x) Sum 1 0.700000 0.700000 2 0.210000 0.910000 3 0.063000 0.973000 4 0.018900 0.991900 5 0.005670 0.997570 6 0.001701 0.999271 7 0.000510 0.999781 Cumulative Probability Distribution x P(X = x) Sum 1 0.700000 0.700000 2 0.210000 0.910000 3 0.063000 0.973000 4 0.018900 0.991900 5 0.005670 0.997570 6 0.001701 0.999271 7 0.000510 0.999781 What is the chance that it takes more than five shots before she makes one? ( 5) 1 .99757 .00243 P X =  = Problem: A basketball player consistently makes 70% of her free throws. In practice one day, she is told to shoot free throws until she makes three baskets. The random variable, X , counts the number of shots she takes before she can stop. P(X = 3) = P(X = 4) = P(X = 5) = . . P(X = x) = x P(X=x) 3 0.3430 4 0.3087 5 0.1852 6 0.0926 7 0.0417 8 0.0175 9 0.0070 10 0.0027 11 0.0010 12 0.0004 13 0.0001 ( 29 ( 29 ( 29 3 3 2 1 ( ) .7 .3 x x P X x C = = x P(X=x) 3 0.3430 4 0.3087 5 0.1852 6 0.0926 7 0.0417 8 0.0175 9 0.0070 10 0.0027 11 0.0010 12 0.0004 13 0.0001 ( 29 ( 29 ( 29 3 3 2 1 ( ) .7 .3 x x P X x C = = What is the probability that it takes between 5 and 10 shots (inclusive) for her to make the three baskets? x P(X=x) 3 0.3430 4 0.3087 5 0.1852 6 0.0926 7 0.0417 8 0.0175 9 0.0070 10 0.0027 11 0.00100....
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 Spring '10
 Wallace

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