d: Define a probabiliry function and state whether a given function satisfies the conditions for a probability function.
The probability functionspecifies the probability that the random variable takes on a specific value.
Example:The following is a probability function:
For X: (1, 2, 3, 4), p(x) = x / 10, else p(x) = 0.
The probabilities are p(1) = 0.1, p(2) = 0.2, p(x) = 0.3, and p(x) = 0.4, all of which are between zero and one. Also, 0.1 + 0.2 + 0.3 + 0.4 = 1.
e: State the two key properties of a probability function.
The two key propertiesof a probability function are:

  1. 0 ≤ p(x) ≤ 1

  2. The sum of all the probabilities for mutually exclusive and exhaustive outcomes must equal one.

f: Define a cumulative distribution function and calculate probabilities for a random variable, given a cumulative distribution function.