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

Step-by-step explanation:

The Poisson distribution formula for probability is given by :-

$P(X=x)=\dfrac{e^{-\lambda}\lambda^x}{x!}$

, 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, $P(X=0)=\dfrac{e^{-1.8}(1.8)^0}{0!}$

$P(X=0)=\dfrac{e^{-1.8}(1)}{1}$

Put value of e= 2.71828

$=(2.71828)^{-1.8}\\\\=0.165298888222\approx0.1653$

Hence, the correct answer is 0.1653  .