Unformatted text preview: X , prove Var[ X ] = E[ X 2 ]E[ X ] 2 . Please prove it for both discrete and continuous cases. Problem 6: For U ∼ Uniform[0 , 1], (1) Calculate cumulative density function F ( u ) = P ( U ≤ u ). (2) Calculate E[ U ], E[ U 2 ], and Var[ U ]. Problem 7: For T ∼ Exponential( λ ), (1) Calculate F ( t ) = P ( T ≤ t ). (2) Calculate E[ T ]. 1...
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 Fall '09
 Wu
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