Assume a random variable XX follows a Poisson distribution with a mean μ=3.7μ=3.7. Find P(X≤4) P(X≤4)=

Question

Question

Assume a random variable XX follows a Poisson distribution with a mean μ=3.7μ=3.7.

Find P(X≤4)

P(X≤4)=

Answer 1

Answer #1

Solution :

Given that mean μ = 3.7

=> P(x <= 4) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4)

= [(e^(-3.7) * 3.7^0)/0! + (e^(-3.7) * 3.7^1)/1! + (e^(-3.7) * 3.7^2)/2! + (e^(-3.7) * 3.7^3)/3! + (e^(-3.7) * 3.7^4)/4!]

= 0.0247 + 0.0915 + 0.1692 + 0.2087 + 0.1931

= 0.6872

Formula :

=> For poisson distribution P(x,μ) = (e^-μ * μ^x)/x!

Answer 2

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