Let X be a Bernoulli rv with pmf as in Example 3.18. a. Compute E(X2). b. Show that V(...

Let X be a Bernoulli rv with pmf as in Example 3.18.

a. Compute E(X2).

b. Show that V(X) = p(1 – p).

c. Compute E(X⁷⁹).

Reference example 3.18

Let X = 1 if a randomly selected vehicle passes an emissions test and X = 0 otherwise.

Then X is a Bernoulli rv with pmf p(1) = p and p(0) = 1 - p , from which E(X) = 0. P(0) + 1. P(1) = 0(1 – p) + 1(p) = p. That is, the expected value of X is just the probability that X takes on the value 1. If we conceptualize a population consisting of 0s in proportion and 1 – p in proportion p, then the population average is µ = p.