Question

Assume a random variable X follows a Poisson distribution with a mean (μ) of 5. What is the probability P(X=1)?

Answer 1

To find the probability P(X=1), we can use the Poisson probability distribution function. In this case, X follows a Poisson distribution with a mean (μ) of 5. The probability P(X=1) is approximately 0.0337.

Step-by-step explanation:

To find the probability P(X=1), we can use the Poisson probability distribution function. In this case, X follows a Poisson distribution with a mean (μ) of 5. The formula for the Poisson probability P(X=k) is:

P(X=k) = (e^(-μ) * μ^k) / k!

Substituting the values into the formula, we have:

P(X=1) = (e^(-5) * 5^1) / 1!

Calculating this, we find that P(X=1) is approximately 0.0337.