Final answer:
The probability of a Poisson random variable with parameter μ=2 being exactly 2 is computed using the relevant Poisson probability mass function and is approximately 0.2707.
Step-by-step explanation:
If x is a Poisson random variable with parameter μ=2, the probability that x equals 2 is given by the Poisson probability mass function (PMF). The formula for the PMF of a Poisson distribution is:
P(x=k) = μ^k * e^(-μ) / k!
Substituting the given parameters μ=2 and k=2 into the formula, we get:
P(x=2) = 2^2 * e^(-2) / 2! = 4 * e^(-2) / 2 = 2 * e^(-2) ≈ 0.2707
The value of e is approximately 2.71828, which is the base of the natural logarithm.