The probability that a Poisson random variable X is equal to 2, where = 7, is
A)( 7! 2!)/9!
B)9!/( 7! 2!)

Question

The probability that a Poisson random variable X is equal to 2, where = 7, is
A)( 7! 2!)/9! 
B)9!/( 7! 2!)

Quizplus · Accepted Answer

The formula for the probability mass function of a Poisson distribution is given by P(X=k) = (e^(-lambda) * lambda^k) / k!. Substituting the given values, we have P(X=2) = (e^(-7) * 7^2) / 2! = 0.161. Therefore, the correct option is C, which corresponds to the calculated probability value in decimal form. The formula for the probability mass function (PMF) of a Poisson distribution is:

P(X = k) = (λ^k * e^-λ) / k!

where λ is the mean and k is the value of the random variable. So for this problem,

P(X = 2) = (7^2 * e^-7) / 2! 
          = 49 * 0.00091188 
          = 0.0447

Therefore, the correct choice is C, which is the closest value to 0.0447.

The Probability That a Poisson Random Variable X Is Equal