The random variable X follows a Poisson distribution with an expected value of 10. What is...
The random variable X follows a Poisson distribution with an expected value of 10. What is P(5 ≤ X ≤ 9)? Include 4 decimal places in your answer.
Homework Answers
Here, λ = 10, x1 = 5 and x2 = 9.
As per Poisson's distribution formula P(X = x) = λ^x *
e^(-λ)/x!
We need to calculate P(5 <= X <= 9)
P(5 <= X <= 9) = (10^5 * e^-10/5!) + (10^6 * e^-10/6!) +
(10^7 * e^-10/7!) + (10^8 * e^-10/8!) + (10^9 * e^-10/9!)
P(5 <= X <= 9) = 0.0378 + 0.0631 + 0.0901 + 0.1126 +
0.1251
P(5 <= X <= 9) = 0.4287
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