If a Poisson random variable X has an average of 5.5, find: p(X=6)
To find p(X=6), we can use the formula for a Poisson distribution:
P(X=k) = (λ^k * e^(-λ)) / k!
where λ is the average number of events in a given time period and k is the value we want to find the probability for.
In this case, λ = 5.5 and k = 6. Plugging these values into the formula, we get:
P(X=6) = (5.5^6 * e^(-5.5)) / 6!
P(X=6) = (5.5^6 * e^(-5.5)) / (6*5*4*3*2*1)
P(X=6) = (386.376 * 0.00408677) / 720
P(X=6) ≈ 0.219
Therefore, the probability of X being equal to 6 is approximately 0.219.