Question

If X has Poisson distribution with parameter m and P(X = 3) = P(X = 4) then m = ____.

Answer 1

If X has Poisson distribution with parameter m and P(X = 3) = P(X = 4) then m = 4.

Explanation:

P(X = k) = `(e^-mm^k)/(k!)` 

where is the number of occurences (k = 0, 1, 2, ...)

P(X = 3) = P(X = 4) 

k = 3 and k = 4

`(e^-mm^3)/(3!)=(e^-mm^4)/(4!)`  

`1/(3!)=m/(4!)`

m = `(4!)/(3!)`

4! = 4 × 3 × 2 × 1 = 24

and 3! = 3 × 2 × 1 = 6 

m = `24/6`

m = 4