Question

The probability mass function of a random variable X, is give by

k λˣ/x!' for x = 0, 1, 2, 3, ...,
where k and A are positive values. Find the value of
A. P(X = 0)
B. P(X > 2)

Answer 1

The student's question involves finding the value of λ for a Poisson distribution's probability mass function, and computing the probability for a given event. The known formulas for Poisson distribution are used to solve for P(X = 0) and P(X > 2). The correct option is A.

Step-by-step explanation:

The student is dealing with a probability mass function (PMF) that takes the form of a Poisson distribution with mean λ. The expression given appears to be λ^x / x! multiplied by a constant k, which stands for the probability that the random variable X equals x for x being a non-negative integer.

To find the value of λ for part A, P(X = 0), we need to consider that for a Poisson distribution, P(X = 0) = e^-λ according to the formula provided.

Part B, P(X > 2), requires using the complement rule where P(X > 2) = 1 - P(X ≤ 2), and then summing the probabilities P(X = 0) + P(X = 1) + P(X = 2) to find P(X ≤ 2) for a Poisson distribution, which is done by adding λ^x / x! for x = 0, 1, and 2 and then subtracting from 1. The correct option is A.