f a Poisson random variable X has an average of 4, find:
0.0298
0.0356
0.0425
0.0187
0.0564
To find the probability of X = 4 for a Poisson random variable, we use the Poisson probability formula:
P(X = k) = (e^(-λ) * λ^k) / k!
where λ is the average (4 in this case) and k is the value we are looking for (4 in this case).
P(X = 4) = (e^(-4) * 4^4) / 4!
Calculating this out, we get:
P(X = 4) = (0.0183 * 256) / 24
P(X = 4) = 0.196
Therefore, the probability of a Poisson random variable with an average of 4 being equal to 4 is 0.196. None of the provided options match this result.