Infant mortality is an example of a relatively rare event that can be described by the Poisson distribution, for which the probability of x occurrences is given by

(a) Verify that ƒ describes a probability distribution by showing that

(b) Calculate the expected value for ƒ, given by

(c) In 2019, the U.S. infant mortality rate was estimated at 5.3 per 1000 live births. Assuming that this is the expected value for a Poisson distribution, find the probability that in a random sample of 1000 live births, there were fewer than 4 cases of infant mortality.

f(x) = Xe x! x = 0, 1, 2, ...