Question

Given a Poisson random variable X, where the average number of successes occurring in a specified interval is 1.8, then P(X = 0) is:

-1.8
-1.3416
-0.1653
-6.05

Answer 1

Answer: 0.1653

Explanation:

The Poisson distribution formula for probability is given by :-

`P(X=x)=(e^(-\lambda)\lambda^x)/(x!)`

, where
`\lambda`= mean of the distribution and x is the number of successes .

Given a Poisson random variable X, where the average number of successes occurring in a specified interval is 1.8.

i.e.
`\lambda=1.8`

Then,
`P(X=0)=(e^(-1.8)(1.8)^0)/(0!)`

`P(X=0)=(e^(-1.8)(1))/(1)`

Put value of e= 2.71828

`=(2.71828)^(-1.8)\\\\=0.165298888222\approx0.1653`

Hence, the correct answer is 0.1653 .