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100BHWIV - STAT 100B HW IV Due Friday Problem 1 Suppose X1...

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STAT 100B HW IV Due Friday Problem 1: Suppose X 1 ,...,X n f ( x ) independently. Let μ = E[ X ], and σ 2 = Var[ X ]. Let ¯ X = 1 n n X i =1 X i , and s 2 = 1 n - 1 n X i =1 ( X i - ¯ X ) 2 . Prove E[ X ] = μ , and E( s 2 ) = σ 2 . Problem 2: Suppose Y i = x i β true + ² i , i = 1 ,...,n , where x i are fixed, β true is an unknown constant. ² i are independent random errors, with E[ ² i ] = 0, Var[ ² i ] = σ 2 . Suppose we want to estimate
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