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A Poisson distribution has a double mode at x = 1 and x = 2. The probability for x = 1 or for x = 2 of these two value is:
1. 4e-2
2. e-2
3. 2e-2
4. 3e-2

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Best answer
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/1!

⇒ P(x = 2) = λ2. e/2!

According to question P(x = 1) = P(x = 2)

λ1. e/1! = λ1. e/2!

⇒ λ1. e = λ2. e/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

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