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If X is a Poisson variate with P(X = 0) = 0.6, then the variance of X is:

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SSC CGL Tier-II ( JSO ) 2019 Official Paper ( Held On : 17 Nov 2020 )
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  1. \(\rm{ln} \left( \dfrac{5}{3} \right)\)
  2. log1015
  3. 0
  4. ln 15

Answer (Detailed Solution Below)

Option 1 : \(\rm{ln} \left( \dfrac{5}{3} \right)\)
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Detailed Solution

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Given

In Poisson distribution

P(X = 0) = 0.6

Formula

Poisson distribution is given by

f(x) = e-λλx/x!

Calculation

P(X = 0) = e-λλ0/0!

⇒ 0.6 = e-λ

⇒ 1/eλ = 6/10 = 3/5

⇒ eλ = 5/3

Taking log on both side

⇒ logeeλ = loge(5/3)

∴ λ = Loge(5/3)

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