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Continuous Random Variable (1)

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Discrete Random Variables Probability Mass Function (PMF)

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

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Discrete Random Variables Cumulative Distribution Function

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PMF to CDF

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Comparison Discrete RV: 1.Zero slope 2.Jumps in CDF Continuous RV: A continuous function

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

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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.

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PDF of X

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Example 3.3

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Expected Value Discrete Random Variable

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Example Find the expected stoppint point of the pointer

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

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Variance and Standard Deviation

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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.

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Definitions

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Properties of Variance/Standard of Deviation

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Discrete Example

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Quiz 3.3

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