8. Let X1, . . . ,Xn be a random sample from the uniform(0, ) distribution. Use the R command set.seed(3333); x=runif(20, 0, 10) to

8. Let X1, . . . ,Xn be a random sample from the uniform(0, θ) distribution. Use the R command set.seed(3333); x=runif(20, 0, 10) to generate a random sample X1, . . . ,X20 from the uniform(0, 10) distribution, and store it into the R object x.

(a) Give the method of moments estimate of θ and the model-based estimate of the population variance σ2.

(Hint. See Example 6.3-1; use mean(x) to compute the sample mean.)

(b) Use var(x) to compute the sample variance S2.

Comment on which of the two estimates (S2 or the model-based) provides a better approximation to the true value of the population variance σ2, which is 102/12, for this data set.