Suppose that X1, X2,..., Xn are i. i.d, N(μ, δ²) and μ and δ² are estimated by the method of maximum likelihood, with resulting estimates μ_hat and δ²_hat. Suppose the bootstrap is used to estimate the sampling distribution of μ_hat.

a. Explain why the boostrap estimate of the distribution of μ_hat is N(μ_hat, δ²_hat/n)

b. Explain why the bootstrap estimate of the distribution of μ_hat -μ is N(0, δ²_hat/n)

c. According to the result of the previous part, what is the form of the boostrap confidence interval for μ , and how does it compare to the exact confidence interval based on the t distribution?