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?

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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,

B(n,p)=Cx×px×1-pn-xnf(x)=Cx×px×1-pn-xn

The value of Cxn is estimated as,

Cxn=n!r!×n-r!

 

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