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?

Asequence {an} is defined recursively, with a1 = 1, a2 = 2 and, for n > 2, an = an-1 an-2 . find the term a241. a) 0 b) 1 c) 2 d) 1 2

It appears that people who are mildly obese are less active than leaner people. one study looked at the average number of minutes per day that people spend standing or walking. among mildly obese people, the mean number of minutes of daily activity (standing or walking) is approximately normally distributed with mean 376 minutes and standard deviation 64 minutes. the mean number of minutes of daily activity for lean people is approximately normally distributed with mean 528 minutes and standard deviation 107 minutes. a researcher records the minutes of activity for an srs of 7 mildly obese people and an srs of 7 lean people. use z-scores rounded to two decimal places to answer the following: what is the probability (image for it appears that people who are mildly obese are less active than leaner people. one study looked at the averag0.0001) that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes? what is the probability (image for it appears that people who are mildly obese are less active than leaner people. one study looked at the averag0.0001) that the mean number of minutes of daily activity of the 6 lean people exceeds 420 minutes?

Aclassmate thinks that solving a system by graphing gives an exact answer when the lines appear to cross at a grid point, but only an approximate answer when they don't. explain why this isn't true.