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18 Joint Dist I - Chapter 5 Joint Distributions April to...

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Click to edit Master subtitle style 9/7/10 Chapter 5 Joint Distributions April 12
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9/7/10 Two Discrete Random Variables The behavior of a random variable is completely described by its distribution. Similarly, the behavior of a pair of random variables is completely described by their joint distribution. The joint distribution of two discrete random variables (say X and Y) is defined as follows:
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9/7/10 Example Suppose the joint distribution of X and Y is given in the table below. Note that we have included row and column sums or “marginal sums” for convenience. Y 1 2 3 4
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9/7/10 Example, cont. a) What do the probabilities in the table add up to? Answer: Like any probability distribution, the probabilities must add up to one. b) Find P(X=2 and Y=2) Answer: 0.04 c) Find P(X=4 and Y=1) Answer: 0.07 d) Find P(X=5 and Y=3) Answer 0 Find P(X=1).
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9/7/10 Marginal distributions Given the joint distribution of two random variables we can determine the individual distributions of each random variable alone.
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