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A Discrete Conditional Expectations Puzzle
Posted:
Jul 15, 1996 5:11 PM


Let x be a discrete real random variable, and suppose that p and q are possibly correlated discrete r.v.'s that may shed light on x.
Prove or (unlikely) disprove: If p and q are independent, conditional on x, then E[xp=p_0] >= E[x] ===> E[xp=p_0] >= E[E[xq]p=p_0] >= E[x].
Note that this is not the law of iterated expectations, but close.
Thanks for any help,
Lones
.. .. .. .. .. .. / L \ O / N \ E / S \ / S \ M / I \ T / H \ / `' `' `' `' `' ` Lones Smith, Economics Department, M.I.T., E52252C, Cambridge MA 02139 (617)2530914 (work) 2536915 (fax) lones@lones.mit.edu



