Finding-the-Mean-of-Discrete-Random-Variable-1.pptx

Statistics and Probability

1. Statistics and Probability Pauline Misty M. Panganiban The Mean of a Discrete Probability Distribution

2. Objectives: Illustrate and calculate the mean of discrete random variable; Interpret the mean of a discrete random variable and Solve problems involving mean of probability distributions.

3. Given the values of the variable X and Y, evaluate the following summations. , ,  

4. The Mean of a Discrete Probability Distribution To find the mean ( ) or the expected value E(x) of a discrete probability distribution, we use the following formula: Where = mean x = value of the random variable P(X) = is the probability value of the random a random variable  

5. Step 1: Construct the probability distribution 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. Illustrative Example:

6. Example 1 Find the mean of the discrete random variable X with the following probability distribution. Step 1: Construct the probability distribution X P(X) 3 1/8 2 3/8 1 3/8 1/8

7. Example 1 Step 2 : Multiply the value of the random variable X by the corresponding probability. X P(X) X • P(X) 3 1/8 3/8 2 3/8 6/8 1 3/8 3/8 1/8

8. Solution to Example 1 Step 3: Add the results obtained in Step 2. =  

9. Example 2 Surgery Patients The probabilities that a surgeon operates on 3, 4, 5, 6, or 7 patients in any day are 0.15, 0.10, 0.20, 0.25, and 0.30, respectively. Find the average number of patients that a surgeon operates on a day.

10. Solution to Example 2 Step 1: Construct the probability distribution for the random variable X representing the number of patients that a surgeon operates on a day. The probabilities that a surgeon operates on 3, 4, 5, 6, or 7 patients in any day are 0.15, 0.10, 0.20, 0.25, and 0.30, respectively. Number of Patients X Probability P(X) 3 0.15 4 0.10 5 0.20 6 0.25 7 0.30

11. Solution to Example 2 Step 2: Multiply the value of the random variable X by the corresponding probability. Number of Patients X Probability P(X) X • P(X) 3 0.15 0.45 4 0.10 0.40 5 0.20 1.00 6 0.25 1.50 7 0.30 2.10

12. Solution to Example 2 Step 3: Add the results obtained in Step 2. The average number of patients that a surgeon will operate in a day is 5.45.  

13. Summary To find the mean of the probability distribution , Construct the probability distribution for the random variable X Multiply the value of the random variable X by the corresponding probability. Add the results obtained in Step 2.

14. Thank you!

15. Illustrative Examples Find the mean of the probability distribution of the random variable X, which can take only the values 1, 2, and 3, given that P(1) = 10/33, P(2) = 1/3 , and P(3) = 12/33.

16. Group Activity The probabilities of a machine manufacturing 0, 1, 2, 3, 4, or 5 defective parts in one day are 0.75, 0.17, 0.04, 0.025, 0.01, and 0.005, respectively. Find the mean of the probability distribution.

17. QUIZ: A bakeshop owner determines the number of boxes of pandesal that are delivered each day. Find the mean of the probability distribution shown. Number of Boxes X Probability P(X) 35 0.10 36 0.20 37 0.30 38 0.30 39 0.10