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    E-Value Expectation and Standard Deviation of a Distribution

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    Billy is collecting bottle caps from his favorite brand of soda pop. The company that produces it runs a contest: each bottle cap shows a picture of one of the 50 states of the United States, with each state equally likely. If you collect all 50 states, then you win a cash prize.

    1. Find the e-value of your distribution of the number of bottle caps needed to get a full set of 50.

    answers:
    a) 204
    b) 225
    c) 286
    d) 301

    2. Find the standard deviation of your distribution of the number of bottle caps needed to get a full set of 50.

    answers:
    a) 62
    b) 67
    c) 74
    d) 79

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    Solution Preview

    Solution.(1) Let X denote the number of bottle caps collected before a complete set is attained. Define Xi, i=0,1,...,49 to be the number of additional bottle caps that need be obtained after i distinct pictures have been collected in ...

    Solution Summary

    cap shows a picture of one of the 50 states of the United States, with each state equally likely. If you collect all 50 states, then you win a cash prize.

    1. Find the e-value of your distribution of the number of bottle caps needed to get a full set of 50.

    answers:
    a) 204
    b) 225
    c) 286
    d) 301

    2. Find the standard deviation of your distribution of the number of bottle caps needed to get a full set of 50.

    answers:
    a) 62
    b) 67
    c) 74
    d) 79

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