If a Poisson random variable X has an average of 5.5 find: p(X=6)
To calculate p(X=6) for a Poisson random variable with an average of 5.5, we use the Poisson probability mass function formula:
P(X = k) = (e^(-λ) * λ^k) / k!
where λ is the average rate of occurrence for the Poisson random variable.
In this case, λ = 5.5 and k = 6. So, plugging into the formula:
P(X = 6) = (e^(-5.5) * 5.5^6) / 6!
Calculating this value gives:
P(X = 6) ≈ 0.139
Therefore, the probability of the Poisson random variable X being equal to 6 when the average is 5.5 is approximately 0.139.