A variable y of a finite population has the following frequency distribution:

y 12 3 4 f 2 2 10 6 Suppose a member is selected at random from the population and let Y denote the value of the variable y for the member obtained.

a. Determine the probability distribution of the random variable Y .

b. Use random-variable notation to describe the events that Y takes on the value 3, a value less than 3, and a value of at least 3.

c. Find P(Y = 3), P(Y < 3), and P(Y ≥ 3). Interpret your results.

d. Construct a probability histogram for the random variable Y .