Question

What is a discrete probability distribution? What two conditions determine a probability distribution?

Answer 1

We need to define discrete probability distribution and find the two conditions that determine it. The probabilities of random variables have discrete values as outcomes in the case of a discrete probability distribution.

Complete step-by-step answer:
We are asked to define the term discrete probability distribution and find the two conditions that determine it. We will be using the concept of probability to solve the given question.
A set of data is said to be discrete if the values belonging to the set can only take certain separated values. The discrete values are usually integers.
Examples:
1. The number of students in a class can only assume a whole number. It cannot be a fraction or a decimal.
The random variable that has a countable number of values is called a discrete random variable.
The discrete distribution represents the probability of occurrence of a discrete random variable. The discrete probability distribution is usually represented in tabular form.
Let us now understand the concept of discrete probability distribution using an example.
Example:
Rolling a die.
The possible outcomes of rolling a die are 1, 2, 3, 4, 5, and 6. All the outcomes have fair or equal chances of occurrence.
The discrete probability distribution table is given as follows,
Odds, in probability, is the ratio of number of favorable outcomes to the number of unfavorable outcomes.

Roll	1	2	3	4	5	6
Odds	1/6	1/6	1/6	1/6	1/6	1/6

The two conditions that determine a probability distribution are given as follows,
1. The sum of all the probabilities should be equal to one.
2. The value of each probability should be greater than or equal to zero.

Note: We must always remember that discrete probability distribution can take only certain values. The applications of probability distributions include calculation of critical regions for hypothesis tests, calculation of confidence intervals for parameters, and determining the distribution model for data.