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APPLIED MATHEMATICS_Discrete

Dicrete probability ddensity function is the type of a random variable that deals with countable domain

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APPLIED MATHEMATICS_Discrete

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  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

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

  9. From

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

  11. Solution

  12. 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

  13. From From series

  14. From series 2 Equation 2 divided by one

  15. From

  16. 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

  17. Let since the median is

  18. Properties of mean Properties of variance

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