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 deviationof 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

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 …

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