Mean (Expectation) of Discrete Random Variable Variance of Discrete Random Variable Standard Deviation of Discrete Random Variable.pptx

Mean (Expectation) of Discrete Random Variable

Variance of Discrete Random Variable

Standard Deviation of Discrete Random Variable

1. Probability and Statistics Second stage- Software department College of Information Technology University of Babylon Dr. Hayder Kadhim Zghair 2020/2021

2. Probability and Statistics- second stage- Software department -College of Information Technology Mathematical Expectation Mean (Expectation) of Discrete Random Variable Variance of Discrete Random Variable Standard Deviation of Discrete Random Variable

3. Probability and Statistics- second stage- Software department -College of Information Technology Mean (Expectation) of Discrete Random Variable Definition 10.1 Let be a discrete random variable with a probability distribution . The mean (or expected value) of is denoted by (or and is defined by:  

4. Probability and Statistics- second stage- Software department -College of Information Technology Example 10.1. Find the mean (expected value) of the discrete random variable where the probability distribution is given by the table below. Solution.   1 2 1 2

5. Probability and Statistics- second stage- Software department -College of Information Technology . . . 0.75  

6. Probability and Statistics- second stage- Software department -College of Information Technology Variance of a Discrete Random Variables Definition 10.2 Let be a discrete random variable with a probability distribution and mean . The variance of is denoted by (or )and is defined by: Note:  

7. Probability and Statistics- second stage- Software department -College of Information Technology Example 10.2. Let be a discrete random variable with the following probability distribution Find the variance of . Solution. .  

8. Probability and Statistics- second stage- Software department -College of Information Technology 1. First method: =(0  0.61) 2 P (0)+(1 0.61) 2 P (1)+(2 0.61) 2 P (2)+ (3 0.61) 2 P (3) =( 0.61) 2 (0.15)+(0.39) 2 (0.38)+(1.39) 2 (0.10)+ (2.39) 2 (0.01) = 0.4979

9. Probability and Statistics- second stage- Software department -College of Information Technology Solution.   2. Second method:  

10. Probability and Statistics- second stage- Software department -College of Information Technology Standard Deviation of Discrete Random Variable Definition 10.3. The positive square root of the variance of is called the Standard Deviation of and is denoted by , i.e., Example 8.3. Find the Standard Deviation of in example 8.2. Solution.  

11. Probability and Statistics- second stage- Software department -College of Information Technology Homework 10. Let be a discrete random variable with the following probability distribution Find the mean (expected value) of . Find the variance of . Find the standard deviation of .  

12. Probability and Statistics- second stage- Software department -College of Information Technology 2. Two dice are tossed together. The random variable denoted to the sum of the two pair. Find the mean (expected value) of . Find the variance of . Find the standard deviation of .