# 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.

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

https://brainmass.com/statistics/quantative-analysis-of-data/value-expectation-standard-deviation-distribution-7309

#### 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