What makes a function of a discrete variable a candidate for a discrete random variable distribution? What about the counterpart of this candidacy in the case of a continuous variable?

A random variable is a variable having numerical values determined by the outcomes of the experiment. A random variable may have a finite number or an infinite sequence of values said to be discrete.

A random variable that describes the number of automobiles sold at a dealership would be discrete one day. Simultaneously, a random variable represents the weight of a person in a kilogram or pounds.

The probability distribution of discrete random variable x is each possible value of x and the probability that x takes amount in one trial of the experiment.

The probability distribution of the random variable contains the following properties:

1- Each probability must be between 0 and 1.

0 ≤ p(x) ≤ 1

2- The sum of all probabilities is equal to 1.

Ʃp(x) = 1

A continuous random variable may assume any value from data. The continuous random variable takes costs that vary within one or more intervals. And it has a cumulative distribution function (CDF) that is absolutely continuous.

The random variable has an infinite number of possible values, which have zero probability. The range of this type of discount can have a nonzero chance.

The probability distribution of the random variable is described by probability density, where the probability can be calculated by taking the area under the curve.