25 chapter 5 exampleadaptedfromexercise583page180

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Unformatted text preview: ility function: ∑ PY|X (y x) = 1 y 24 and ∑ PX|Y (x y ) = 1 x Chapter 5 The random variables X and Y are independent if and only if: PX , Y (x , y) = PX (x) PY (y) for all pairs (x, y) If random variables X and Y are independent then: PY|X (y x ) = = PX , Y (x , y ) PX (x) PX (x ) PY (y ) PX (x ) = PY (y ) That is, the conditional probability function of Y, given that the random variable X takes the value x, is identical to the marginal probability function of Y, for all possible values of y. 25 Chapter 5 Example: Adapted from Exercise 5.83, page 180 A survey by a real estate agent has collected information on apartment rentals. Consider the discrete random variables: X volume of inquiries by renters. The possible values are: x = 0 little interest x = 1 moderate interest x = 2 strong interest Y number of lines in a newspaper ad. Possible values are: y = 3, 4, 5 The joint probability function is: X Y 0 1 2 3 0.09 0.14 0.07 4 0.07 0.23 0.16 5 0.03 0.10 0.11 26 Chapter 5 Questions and Answers • Find the probability function of X. PX (0) = 0.09 + 0.07 + 0.03 = 0.19 PX (1) = 0.14 + 0.23 + 0.10 =...
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