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Conditional expectation

  1. Feb 24, 2010 #1
    Question 1)

    I have X and Y independent stoch. variables

    What is E[X^2 * Y | X] ?

    does it generally hold that if X and Y are independent, then every function of X (eg X^2) is independent of Y?

    Does E[X^2 * Y | X] then become E[X^2|X]*E[Y|X] = E[X^2|X]*E[Y] since X^2 is independent of Y?

    I'm stuck here... (If the above is correct, what is E[X^2|X)?

    Question 2)

    B(t) is Brownian motion (starting at 0), and 0<t1<t2<t3<t4

    E[B(t4)-B(t2) | B(t3)-B(t1)] = ?

    I'm stuck here because I don't know what the expression evaluates to when the intervals overlaps. E[B(t4)-B(t3) | B(t2)-B(t1)] = E[B(t4)-B(t3)] = 0 since the intervals are disjoint...? But what about the above expression?

    Thank you
  2. jcsd
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