Question

A certain brand of upright freezer is available in three different rated capacities: 16 ft3, 18 ft3, and 20 ft3. Let X = the rated capacity of a freezer of this brand sold at a certain store. Suppose that X has the following pmf.

x 16 18 20
p(x) 0.5 0.3 0.2
Calculate E(X)

Answer 1

E(X) = 17.4

Explanation:

We can calculate the expected value of a random X variable that is discrete (X takes specific values ) as:

E(X) = ∑xp(x) where x are the specific values of x and p(x) the probability associated with this x value.

In this way the expexted value is

E(X) = ∑xp(x) =(16*0.6)+(18*0.3)+(20*0.2) = 8+5.4+4 = 17.4