17. The monthly proportion of purchases paid by check to a large grocery store that are returned because of insufficient funds can be viewed as the outcome of a Beta(1, 20)

distribution.

(a) Simulate 12 monthly proportions of returned checks using the following 24 outcomes from a Uniform(0,1)

computer random number generator:

(.6829,.4283,.0505,.7314,.8538,.6762,.6895,.9955,.2201,

.9144,.3982,.9574,

.0801,.6117,.3706,.2936,.2799,.3900,.7533,.0113,.5659,

.9063,.5029,.6385)

(Hint: In a previous problem you have proven that Y ¼ X1/(X1 + X2) has a beta distribution with parameters (a,b) if (X1, X2) are independent gamma-distributed random variables with parameters

(a,

b) and

(b, b), respectively.)

(b) Calculate the sample mean and sample variance, and compare them to the appropriate population mean and variance.