A friend of ours takes the bus five days per weekto her job. The five waiting times until she canboard the bus are a random sample from a uniformdistribution on the interval from 0 to 10 min.a. Determine the pdf and then the expectedvalue of the largest of the five waiting times.b. Determine the expected value of the differ-ence between the largest and smallest times.c. What is the expected value of the samplemedian waiting time?d. What is the standard deviation of the largesttime?

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T job. The five wait d the bus are a random bution on the interva etermine the pdf a

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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

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Question

A friend of ours takes the bus five days per week
to her job. The five waiting times until she can
board the bus are a random sample from a uniform
distribution on the interval from 0 to 10 min.
a. Determine the pdf and then the expected
value of the largest of the five waiting times.
b. Determine the expected value of the differ-
ence between the largest and smallest times.
c. What is the expected value of the sample
median waiting time?
d. What is the standard deviation of the largest
time?

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