FM5002-HW9-4.11.12

# 4 46 15 0 which is to be expected sin ce x an d yare

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Unformatted text preview: X, Y = E[XY − E[X] E[Y = ((−3) (0.1) + (−6) (0.1) + (−5) (0.4) + (−10) (0.4)) − (4.6) (−1.5) = 0, which is to be expected, sin ce X an d Yare indepen dent. 0049− . Fin d two PCRVs X an d Ysuch that E[X | Y is determin istic, but X an d Yare not in dependent. 4 Let Y Ω 0 if 0 Ω 0.5 and X Ω 1 if 0.5 Ω 1 0 if 0 Ω 0.25 2 if 0.25 Ω 0.5 . 1 if 0.5 Ω 1 Then E[X | Y = 1, but E[X = 0 | Y= 0] = 0.5 != E[X = 0] = 0.25. 0049− . Fin d two PCRVs X an d Ysuch that E[XY = E[X] E[Y but E[X | Y is n ot deterministic. 5, Let X t so that E XY 1 if 0 t 1 3 0 if 1 3 t 2 3 and Y t 1 if 2 3 t 1 E X E Y . But E X Y 0 if 0 t 1 3 1 if 1 3 t 2 3 . Then E X 0 if 2 3 t 1 X t , which is n ot determin istic. 0 an d E X Y 0,...
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## This note was uploaded on 01/19/2014 for the course MATH 5002 taught by Professor Adams during the Spring '08 term at Minnesota.

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