Question

Find the mean of x if x is a Poisson variate satisfying the condition P(3) = P(4)?
1. 2
2. 8
3. 4
4. 16

Answer 1

Correct Answer - Option 3 : 4

Given

P(3) = P(4)

Concept

In poisson distribution = it is also a discrete distribution. Poisson distribution fulfil the limitation of nomal distribution

Poisson distribution is given by f(x) = (e^-λ × λ^x)/x!

Where x = 0, 1, 2, 3---- and λ = mean

Calculation

Here x = 3 and 4

⇒ (e^-λ × λ³)/3! = (e^-λ × λ⁴)/4!

⇒ λ  = 4!/3!

⇒ λ = 4

∴ mean of x in poisson distribution is 4