Question

Assume that the time between two consecutive accidents in a chemistry lab follows an exponential distribution with parameter λ. Starting to count from the day of the first accident (this will be day 0), there has been accidents on the 28th, 50th, 60th days. Compute the maximum likelihood estimate of λ. Explain the steps.

Answer 1

Answer:-

Given that:-

X: The time between two consecutive accidents.

the pdf of X is given by ,

There has been accidents an  days

here n= 2 and

The likelihood function for is,

where;

is the sample mean

The loglikelihood function for is

We can find maximum likelihood estimator of by taking partial dirivative of log likelihood function with respect to and equate it to zero.

i.e.,

is maximum likelihood estimator of

Sample mean