Question

Problem 3: A telemarketing firm is interested in estimating the probability of a sale, $p$. Let $X_i$ be the number of phone calls without a sale before 3 sales are made in the $i^{th}$ day. Assume $X_1, \dots, X_n$ a random sample from a negative binomial $(3, p)$ where $0 \le p \le 1$ and $p$ is unknown. Four data points were observed: 12, 17, 7, 19. (a) Derive the method of moments estimator of $p$. (b) Compute the method of moment estimate of $p$. (c) Find the ML estimator of $p$. (d) Find the ML estimate of the standard deviation of $X$.

          Problem 3:
A telemarketing firm is interested in estimating the probability of a sale, $p$. Let $X_i$ be the number
of phone calls without a sale before 3 sales are made in the $i^{th}$ day. Assume $X_1, \dots, X_n$ a
random sample from a negative binomial $(3, p)$ where $0 \le p \le 1$ and $p$ is unknown. Four data
points were observed: 12, 17, 7, 19.
(a) Derive the method of moments estimator of $p$.
(b) Compute the method of moment estimate of $p$.
(c) Find the ML estimator of $p$.
(d) Find the ML estimate of the standard deviation of $X$.

Problem 3:
A telemarketing firm is interested in estimating the probability of a sale, p. Let Xi be the number
of phone calls without a sale before 3 sales are made in the i^th day. Assume X1, …, Xn a
random sample from a negative binomial (3, p) where 0 ≤ p ≤ 1 and p is unknown. Four data
points were observed: 12, 17, 7, 19.
(a) Derive the method of moments estimator of p.
(b) Compute the method of moment estimate of p.
(c) Find the ML estimator of p.
(d) Find the ML estimate of the standard deviation of X.

Added by Janice S.

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