Question

Let $X_{1}, X_{2}, \dots, X_{n}$ be random sample from a Poisson family with parameter $\lambda$. Then the maximum likelihood estimate of $P(X \ge 2)$ is

• A. $1 - \overline{X} e^{-\overline{X}}$
• B. $(1 + \overline{X}) e^{-\overline{X}}$
• C. $\overline{X} e^{-\overline{X}}$
• D. $1 - (1 + \overline{X}) e^{-\overline{X}}$

Hint:

The MLE invariance property is extremely powerful: simply find the MLE of the basic parameter and plug it into whatever formula or probability you are asked to estimate.

Answer 1

The Correct Option is D