 Solution

ID: past-exam-of-the-probability-statistics-and-options-i-course-of-the-university-of-oxford/2011/m/3/c/iii/solution

From the preceding decomposition,

Y = (3/5) X + W

, where

W

is independent of

X

and has mean zero. Taking conditional expectation gives

E [Y ∣ X] = (3/5) X

. The corresponding continuous version at

X = 5

E [Y ∣ X = 5] = 3.

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