Question

The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. The probability that there are 8 occurrences in ten minutes is _________.

Answer 1

Answer:

The probability that occurrence of 8 in ten minutes is 0.0771.

Step-by-step explanation:

Poisson Distribution:

A discrete random variable X having the enumerable set {0,1,2,.....} as the spectrum, is said to have Poisson distribution with parameter $\mu$ (>0), if the p.m.f is given by

$P(X=x)=\frac{e^{-mu}\mu^x}{x!}$  for x=0,1,2,...

               = 0,           elsewhere

The mean number of occurrences in ten minutes is 5.3.

Here $\mu$ = 5.3 and x= 8

$P(X=8)=\frac{e^{-5.3}(5.3)^8}{8!}$

               =0.0771

The probability that occurrence of 8 in ten minutes is 0.0771.