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Chapter 5: Problem 6

Explain the meaning of the probability distribution of a discrete random variable. Give one example of such a probability distribution. What are the three ways to present the probability distribution of a discrete random variable?

Short Answer

Expert verified
The probability distribution of a discrete random variable is a means to assign probabilities to the possible outcomes of the variable. An example is the tossing of a fair die, with each outcome having an equal likelihood of 1/6. The distribution can be presented in three common ways, namely in a tabular form, by using a graph or as a function.

Step by step solution

01

Definition of Probability Distribution

The probability distribution of a discrete random variable is a list, graph, or function that assigns a probability to each possible outcome of the discrete variable. In other words, it describes how probabilities are distributed over values of a discrete random variable.
02

Example of Probability Distribution

An example of such a probability distribution is the tossing of a fair die. Here, the random variable, which can be defined as the outcome of the toss, can take values from 1 to 6 which are mutually exclusive and exhaustive. The probabilities here are \( P_{1} = P_{2} = P_{3} = P_{4} = P_{5} = P_{6} = \frac{1}{6} \). This is a uniform probability distribution because all outcomes are equally likely.
03

Ways to Present Probability Distribution

There are three common ways to present the probability distribution of a discrete random variable: \n\na) Tabular form: where the values of the random variable are listed against their corresponding probabilities in a table. \n\nb) Graphical form: here the probabilities are plotted against the corresponding values of the random variable on a graph, often resulting in a histogram or bar chart. \n\nc) Function form: a function may be defined to explicitly denote the relationship between the random variable and its probability.

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