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: