APPLIED MATHEMATICS_Discrete

1. APPLIED MATHEMATICS DISCRETE RANDOM VARIABLE

2. Properties of a discrete random variable If is a random variable , then Example Given that a coin is thrown three times and is the number of heads that are obtained

3. H T H H T H T H T H T T H T

4. ( TTT)

5. The above information can be best illustrated in table form The mean of a discrete random variable The mean of a discrete random variable is sometimes called expectation denoted by and is given by

6. Variance and standard deviation Where

7. Example A random variable x has the following distribution Find the mean and variance of x Solution

9. Example : The random variable x takes integral values only and has a pdf . Find • The value of constant k • Variance of Solution

10. From

12. Example A discrete random variable X has a pdf as shown in the table below. Determine • The value of constant a

13. Solution

14. Example The discrete random variable X has a pdf Where k is a constant. Given that the expectation of is 3. Find • The value of n and the constant k. • The median of variance of Solution

15. From From series

16. From series 2 Equation 2 divided by one

17. From

18. Cumulative Mean Function The cumulative mean function of a discrete random variable is given by The median is the smallest value of for which Where is the cumulative function

20. Let since the median is

21. Properties of mean Properties of variance