The probability that a Poisson random variable X is equal to 4, where = 10, is

Question

The probability that a Poisson random variable X is equal to 4, where  = 10, is

Quizplus · Accepted Answer

The probability mass function (PMF) of a Poisson random variable is given by:

P(X=k) = (lambda^k * e^(-lambda)) / k!

where lambda is the mean and variance of the Poisson distribution.

In this case, lambda = 10 (given).

So,

P(X=4) = (10^4 * e^(-10)) / 4!

= (10000/24) * e^(-10)

= 0.018132788...

Rounding to 4 decimal places gives:

P(X=4) = 0.0181

which is closest to the value in choice C:

11eaa984_72b3_e215_97c0_a111f54a74ff_TB1705_11

The Probability That a Poisson Random Variable X Is Equal