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Continuous Random Variable (1)

Continuous Random Variable (1). Section 3.1-3.3. Continuous Random Variable. What is the probability that X is equal to x ?. CDF for a Discrete Random Variables. Question: Is there a CDF for a continuous random variable if a PMF can not be identified for a continuous random variable?.

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Continuous Random Variable (1)

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  1. Continuous Random Variable (1) Section 3.1-3.3

  2. Continuous Random Variable What is the probability that X is equal to x?

  3. CDF for a Discrete Random Variables Question: Is there a CDF for a continuous random variable if a PMF can not be identified for a continuous random variable?

  4. CDF for a Wheel-Spinning Experiment P[X=≤ x]=x if 0≤X≤1

  5. CDF for Continuous Random Variable • Even though it is not possible to define a PDF for a continuous random variable, it is possible to define a CDF for a random variable

  6. PMF to CDF for a Discrete Random Variable

  7. Theorem 2.2 Theorem 2.3 What contributes to the jump in the CDF?

  8. Discrete RV Continuous RV

  9. Compare CDF of a Continuous RV to that of a Discrete RV Discrete RV: Zero slope Jumps in CDF Continuous RV: A continuous function

  10. Slope of CDF function The slope at any point x indicates the probability that X is near x. (Just as the jump in the CDF of a discrete RV suggests non-zero probability at X=x, so does a slope in CDF of a continuous random variable?)

  11. 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.

  12. Properties of fX(x)

  13. PDF of X

  14. Expected Value Discrete Random Variable

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