Question

If X is a Poisson variate with P(X = 0) = 0.6, then the variance of X is:
1. \(\rm{ln} \left( \dfrac{5}{3} \right)\)
2. log₁₀15
3. 0
4. ln 15

Answer 1

Correct Answer - Option 1 : \(\rm{ln} \left( \dfrac{5}{3} \right)\)

Given

In Poisson distribution

P(X = 0) = 0.6

Formula

Poisson distribution is given by

f(x) = e^-λλ^x/x!

Calculation

P(X = 0) = e^-λλ⁰/0!

⇒ 0.6 = e^-λ

⇒ 1/e^λ = 6/10 = 3/5

⇒ e^λ = 5/3

Taking log on both side

⇒ log_ee^λ = log_e(5/3)

∴ λ = Log_e(5/3)