Question

For a poission variate x, p(x=1) =p(x=2).Find p(x=5)​

Answer 1

ANSWER

Given a poisson variable satisfies P(X=1)=P(X=2)

The probability mass function of the poisson distribution can be defined as f(x)=  

x!

e  −λ  λ  x

 where λ is a parameter.

Consider P(X=1)=P(X=2)

⇒  1! e   λ  = ! e  −λ  λ  

 

​  ⇒1=  

2

λ

​  

 

⇒λ=2

Thus P(X=5)=  

5!

e  

−2

2  

5

 

​  

=0.0017