Please explain Suppose a light bulb producer wishes to estimate p, the probability that a certain type of light bulb burns out within 900 hours. 500 bulbs are used for 900 hours each, and 31 of them burn out. What is the maximum likelihood estimate of p?

Please explain Suppose a light bulb producer wishes to estimate p, the probability that a certain type of light bulb burns out within 900 hours. 500 bulbs are used for 900 hours each, and 31 of them burn out. What is the maximum likelihood estimate of p?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

Please explain

Suppose a light bulb producer wishes to estimate p, the probability that a certain type of light bulb burns out within 900 hours. 500 bulbs are used for 900 hours each, and 31 of them burn out. What is the maximum likelihood estimate of p?

Expert Solution

Step 1

Given:

The value of $n$ is 500.

The value of $x$ is 31.

For $binomial$ distribution the equation as,

$\begin{array}{rcl} B (n, p) & = & {}^{n}{C_{x} \times p^{x} \times {(1 - p)}^{n - x}} \\ f (x) & = & {}^{n}{C_{x} \times p^{x} \times {(1 - p)}^{n - x}} \end{array}$

The value of ${}^{n}C_{x}$ is estimated as,

${}^{n}C_{x} = \frac{n!}{r! \times (n - r)!}$

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