Question

2. (Moment estimators of binomial distribution) Let the sample $X_1, \dots, X_n$ follow the distribution \newline Binomial($n, p$), with unknown $n, p$. (a) Provide moment estimators of $n$ and $p$. (Hint: consider both the sample mean and sample variance.) (b) Are the estimators obtained in (a) unbiased?

          2. (Moment estimators of binomial distribution) Let the sample $X_1, \dots, X_n$ follow the distribution \newline Binomial($n, p$), with unknown $n, p$.
(a) Provide moment estimators of $n$ and $p$.
(Hint: consider both the sample mean and sample variance.)
(b) Are the estimators obtained in (a) unbiased?

2. (Moment estimators of binomial distribution) Let the sample X1, …, Xn follow the distribution Binomial(n, p), with unknown n, p.
(a) Provide moment estimators of n and p.
(Hint: consider both the sample mean and sample variance.)
(b) Are the estimators obtained in (a) unbiased?

Added by Mireia C.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sri K

03/16/2023

Step 1

The sample mean of a binomial distribution is np, and the population mean is also np. Therefore, the moment estimator of p is the sample mean divided by n, which is X̄/n. The moment estimator of n can be obtained by equating the sample variance to the population Show more…

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2. (Moment estimators of binomial distribution) Let the sample X,...,Xn follow the distribution Binomial(n, p), with unknown n, p. (a) Provide moment estimators of n and p. (Hint: consider both the sample mean and sample variance.) (b) Are the estimators obtained in (a) unbiased?