Tutorial on Discrete Probability Distributions

Tutorial on discrete probability distributions with examples and detailed solutions.

Discrete Probability Distribution

Let X be a discrete random variable that takes the numerical values X1, X2, ..., Xn with probabilities p(X1), p(X2), ..., p(Xn) respectively. A discrete probability distribution consists of the values of the random variable X and their corresponding probabilities P(X).
The probabilities P(X) are such that
P(X) = 1

Example 1

Let the random variable X represents the number of boys in a family.
a) Construct the probability distribution for a family of two children.
b) Find the mean and standard deviation of X.

Solution to Example 1


Example 2

Two balanced dice are rolled. Let X be the sum of the two dice.
a) Obtain the probability distribution of X.
b) Find the mean and standard deviation of X.

Solution to Example 2


Example 3

Three coins are tossed. Let X be the number of heads obtained. Construct a probability distribution for X and find its mean and standard deviation.

Solution to Example 3


More References and links

elementary statistics and probabilities.