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# E-Value Expectation and Standard Deviation of a Distribution

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.

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.

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

#### 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 order to obtain ...

#### 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.

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.