As in Example 9 1, let h (p) p (1 p) a Find the remainder term in the Taylor expansion, xa (x t) h (t)dt, and use it to find an exact expression for h() b Is the remainder term likely to be smaller than the other terms Explain c Find an exact expression for V h () for a simple random sample with re...

a Since ht 2t the remainder term is Thus b The remainder term is likely to be smaller than the other ...

As in Example 9.1, let h (p) = p (1 p). a. Find the remainder term

Question:

As in Example 9.1, let h (p) = p (1 − p).
a. Find the remainder term in the Taylor expansion, ʃxa (x − t) h” (t)dt, and use it to find an exact expression for h(Ṕ).
b. Is the remainder term likely to be smaller than the other terms? Explain.
c. Find an exact expression for V [h (Ṕ)] for a simple random sample with replacement. How does it compare with the approximation in Example 9.1? Use moments of the Binomial to find E (Ṕ 4).
Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...