Based on past results found in the Information PleaseAlmanac, there is a 0.1919

Question

Based on past results found in the Information PleaseAlmanac, there is a 0.1919 probability that a baseball World Seriescontest will last four games, a 0.2121 probability that it will last five games, a 0.2222 probability it will last six games, and a 0.3737 probability that it will last seven games.

A. does the given information describe a probability distribution?
B. assuming that the given information describes a probability distribution, find the mean and standard deviation for teh numbers of games in world series contests.
C. is it unusual for a team to sweep by winning in four games? why or why not?

Explanation / Answer

The probability distribution of x is :

x p(x)
4 0.1919
5 0.2121
6 0.2222
7 0.3737

Mean = E(x) =
[ (4) ( 0.1919) + (5) (0.2121) + (6) (0.2222) + (7) (0.3737) ] = 5.7772

E(x^2) = [ (4)^2 ( 0.1919) + (5)^2 (0.2121) + (6)^2 (0.2222) + (7)^2 (0.3737) ] = 34.6834
Variance (x) = E(x^2) - mean^2 = 34.6834 - (5.7772)^2 = 1.3074
Standard deviation = square root of variance = 1.1434

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