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Continuous Random Variable (1)

Continuous Random Variable (1). Discrete Random Variables. Probability Mass Function (PMF). Continuous Random Variable. P[X=x]=0. Not possible to define a PMF for a continuous random variable. Discrete Random Variables. Cumulative Distribution Function. PMF to CDF. Comparison .

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Continuous Random Variable (1)

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  1. Continuous Random Variable (1)

  2. Discrete Random Variables • Probability Mass Function (PMF)

  3. Continuous Random Variable P[X=x]=0 Not possible to define a PMF for a continuous random variable

  4. Discrete Random Variables • Cumulative Distribution Function

  5. PMF to CDF

  6. Comparison Discrete RV: Zero slope Jumps in CDF Continuous RV: A continuous function

  7. Slope of CDF function The slope at any point x indicates the probability that X is near x.

  8. Probability Density Function (PDF) It is not possible to define a PMF function for a continuous variable because P[X=x]=0. We can, however, define a probability density function.

  9. PDF of X

  10. Example 3.3

  11. Expected Value Discrete Random Variable

  12. Example Find the expected stoppint point of the pointer

  13. The Expected Value of a function Derived Discrete Random Variable Discrete Example Derived Continuous Random Variable

  14. Variance and Standard Deviation

  15. Key Points • An average is a typical value of a random variable. • The next question: • “What are the chances of observing an event far from the average?” • The variance of a random variable X describes the difference between X and its expected value.

  16. Definitions

  17. Properties of Variance/Standard of Deviation

  18. Discrete Example

  19. Quiz 3.3

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