Jointly distributed random variables

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13 Terms

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Joint Cumulative Distribution Function

  • Recap: the CDF tells you the probability that a random variable is less than or equal to a value P(X<= x)


<ul><li><p>Recap: the CDF tells you the probability that a random variable is less than or equal to a value P(X&lt;= x) </p></li></ul><p></p>
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Joint Probability Mass Function

  • For a pair of random variables X and Y, the sample space S consists of all pairs (x,y) that can be derived from the ranges of X and Y

  • The joint PMF determines how probability is assigned to all pairs of values (x,y)


<ul><li><p>For a pair of random variables X and Y, the sample space S consists of all pairs (x,y) that can be derived from the ranges of X and Y</p></li><li><p>The joint PMF determines how probability is assigned to all pairs of values (x,y) </p></li></ul><p></p>
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Marginal Distribution

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Joint Probability Density Function

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Joint PDF as a function of the CDF

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Marginal probability density function

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If X and Y are independent …

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Independence in terms of PMF/PDF

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Extending to more than two variables

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Conditional Distributions

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Validity of the PDF/PMF for conditional distributions

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Expectation for a function of two random variables

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Properties of the expectation

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