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?

20

step-by-step explanation:

4 and 5)16.97 or 12√2

6)15.59 or 9√3

7)y = 15.59 or 9√3     x =27

8)17.80

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)  

- both graphs increase on their domain.

- the graphs of both functions have the same x-intercept.

- neither graph has a y-intercept.