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

Suppose a member is selected at random from the population and let X denote the value of the variable x for the member obtained.
a. Determine the probability distribution of the random variable X.
b. Use random-variable notation to describe the events that X takes on the value 2, a value of at most 2, and a value greater than 2.
c. Find P(X = 2), P(X ≤ 2), and P(X > 2). Interpret your results.
d. Construct a probability histogram for the random variable X.

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