2010100AHW6

2010100AHW6 - T t ). (2) Calculate E[ T ] and Var[ T ]. (3)...

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STAT 100A HWVI Problem 1: For continuous random variable X , (1) Prove E[ aX + b ] = a E[ X ] + b . (2) Prove Var[ aX + b ] = a 2 Var[ X ]. (3) Prove Var[ X ] = E[ X 2 ] - E[ X ] 2 . (4) Let μ = E[ X ], σ 2 = Var[ X ], and Z = ( X - μ ) . Calculate E[ Z ] and Var[ Z ]. Problem 2: For U Uniform[0 , 1], calculate E[ U ], E[ U 2 ], Var[ U ], and F ( u ) = P ( U u ). Problem 3: For T Exponential( λ ), (1) Calculate F ( t ) = P (
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Unformatted text preview: T t ). (2) Calculate E[ T ] and Var[ T ]. (3) If U Uniform[0 , 1], let X =-log U/ . Calculate F ( x ) = P ( X x ), and f ( x ) = F ( x ). What is the distribution of X ? Problem 4: Suppose Z N(0 , 1). Calculate E[ Z ] and Var[ Z ]. 1...
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This note was uploaded on 01/11/2011 for the course STAT 100A taught by Professor Wu during the Fall '10 term at UCLA.

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