Tutorial on discrete probability distributions with examples and detailed solutions.

Let X be a random variable that takes the numerical values X1, X2, ..., Xn with probablities 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:

a) We first construct a tree diagram to represent all possible distributions of boys and girls in the family.

Assuming that all the above possibilities are equally likely, the probabilities are:

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:

The tree diagram representing all possible outcomes when three coins are tossed is shown below.

Assuming that all three coins are indentical and all possible outcomes are equally likely, the probabilities are: