As in Example 9 1, let h (p) p (1 p) 1 Find the remainder term in the Taylor expansion, xa (x t) h (t)dt, and use it to find an exact expression for h() 2 Is the remainder term likely to be smaller than the other terms Explain 3 Find an exact expression for V h () for a simple random sample with re...

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

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

Question:

As in Example 9.1, let h (p) = p (1 − p).

1. 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).

2. Is the remainder term likely to be smaller than the other terms? Explain.

3. 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 distribution to find E (Ṕ 4). Discuss.

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...