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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.

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 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.

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 ...

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###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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