Constructing Probability Distribution.pptx

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1. Constructing a Probability Distribution Prepared by: Teddy B. Catimbang

2. Lesson Objectives: Illustrate a probability distribution for a discrete random variables and its properties. Compute probabilities corresponding to a given random variable. Construct the probability mass function of a discrete random variable and its corresponding histogram.

3. Probability Distribution A discrete probability distribution or a probability mass function consists of the values a random variable can assume and corresponding probabilities of the values.

4. Example: Suppose three coins are tossed. Let Y be the random variable representing the number of tails that occur. Find the probability of each of the values of the random variable Y.

5. Possible Outcomes Values of the Random Variable Y (Number of tails) TTT 3 TTH 2 THT 2 HTT 2 HHT 1 HTH 1 THH 1 HHH

6. There are four possible values of the random variable Y representing the number of tails. These are 0, 1, 2, and 3. Assign probability values P(Y), to each value of the random variable. There are 8 possible outcomes and no tail occurs once, so the probability that we shall assign to the random variable 0 is There are 8 possible outcomes and 1 tail occurs three times, so the probability that we shall assign to the random variable 1 is . There are 8 possible outcomes and 2 tail occurs three times, so the probability that we shall assign to the random variable 1 is . There are 8 possible outcomes and 3 tail occurs once, so the probability that we shall assign to the random variable 3 is  

7. Properties of Probability Distribution The probability of each value of the random variable X must be between 0 and 1 or equal to 0 or 1. In symbol, we write it as . The sum of the probabilities of all values of the random variable X must be equal to 1. In symbol, we write it as