4. Suppose that X1, . . . , Xn is a sample from a distribution whose variance 2 is unknown. Suppose we are planning to

4. Suppose that X1, . . . , Xn is a sample from a distribution whose variance

σ2 is unknown. Suppose we are planning to estimate σ2 by the sample variance S2 =

n i=1(Xi − ¯ X)2/(n − 1), and we want to use the bootstrap technique to estimate Var(S2).

a. If n = 2 and X1 = 1 and X2 = 3, what is the bootstrap estimate of Var(S2)?

b. If n = 15, and the data values are 5, 4, 9, 6, 21, 17, 11, 20, 7, 10, 21, 15, 13, 8, 6 use simulation to obtain the bootstrap estimate of Var(S2).