Correct Answer - Option 1 : 4e
-2
Formula
Poisson distribution = P(X = x) = [ e-m mx/x! for x = 0, 1, 2, 3 -----]
[ 0 ; otherwise]
Calculation
Poisson distribution has 2 modes at x = 1 and x = 2 it means they have same frequency at x = 1 and 2and have same probability
P(x = 1) = λ1. e-λ/1!
⇒ P(x = 2) = λ2. e-λ/2!
According to question P(x = 1) = P(x = 2)
λ1. e-λ/1! = λ1. e-λ/2!
⇒ λ1. e-λ = λ2. e-λ/2
⇒ λ = 2
⇒ P(x = 1) = 21. e-2/1!
⇒ 2e-2
⇒ P(x = 2) = 22. e-2/2!
⇒ 2.e-2
⇒ P(x) = P(x = 1) + P(x = 2)
⇒ 2e-2 + 2.e-2
∴ P(x) = 4e-2