3.1 Probability Distributions

3.1 PROBABILITY DISTRIBUTIONS by Suhaila Bahrom Department of Mathematics Centre for Foundation Studies, IIUM Learning Objectives Construct a probability distribution table for a discrete random variable. Show probability distribution graphically. Prepared by Suhaila Bahrom_MathDept_CFSIIUM Probabilty Distribution A discrete random variable is random variable which takes a fixed number of countable values. Example: The number of balls taken from the box. The probability distribution of a discrete random variable X is a list of all possible values of the random variable X and their corresponding probabilities. Prepared by Suhaila Bahrom_MathDept_CFSIIUM Consider an experiment where 3 coin are flipped simultaneously. The possible outcomes are tabulated where H denotes a head and T denotes a tail. Let x denotes the number of heads. The probability distribution of X is Prepared by Suhaila Bahrom_MathDept_CFSIIUM Properties of Discrete Probabilty Distribution Line graph Prepared by Suhaila Bahrom_MathDept_CFSIIUM Example 1 A discrete random variable X has probability function (a) Determine the value of the constant b (b) Calculate Prepared by Suhaila Bahrom_MathDept_CFSIIUM Example 2 A discrete random variable X represent the number of even numbers that obtained when two fair dice are tossed. Tabulate the probability distribution of X. Prepared by Suhaila Bahrom_MathDept_CFSIIUM Example 3 A committee consisting of 4 people will be chosen at random from 6 men and 3 women. Let X represent the number of men selected. Construct the probability distribution table of X Prepared by Suhaila Bahrom_MathDept_CFSIIUM Example 4 A fair dice is rolled once. If the score is 2 or more, then X is the score. If the score is 1 then the dice is rolled once again and X is the sum of the scores from two rolls. Construct a probability distribution table of X. Prepared by Suhaila Bahrom_MathDept_CFSIIUM Exercise 1 Madam Mar erases the amount of money that is written on the 3 envelopes containing RM50 note and 2 envelopes containing RM10. She then keeps all the envelopes in a bag. She later discovers that the envelopes are identical. Let X be the number of envelopes she now needs to open in order to have RM10. (a) Draw tree diagram to show all possibilities. (b) Identify all the possible values of X and hence set up the probability distribution table of X. (c) Find the probability that Madam Mar has to open at least 3 envelopes in order to have RM10 note. Prepared by Suhaila Bahrom_MathDept_CFSIIUM