Unformatted text preview: p ( y ) = ( 1 n y = 1 , 2 ,...,n otherwise . Therefore, by deﬁnition, E ( Y ) = n X y =1 yp ( y ) = n X y =1 y 1 n = 1 n n X y =1 y = 1 n n ( n + 1) 2 = n + 1 2 E ( Y 2 ) = n X y =1 y 2 p ( y ) = n X y =1 y 2 1 n = 1 n n X y =1 y 2 = 1 n n ( n + 1)(2 n + 1) 6 = ( n + 1)(2 n + 1) 6 Var( Y ) = E ( Y 2 )[ E ( Y )] 2 = ( n + 1)(2 n + 1) 6³ n + 1 2 ´ 2 = 2 n 2 + 3 n + 1 6n 2 + 2 n + 1 4 = 4 n 2 + 6 n + 23 n 26 n3 12 = n 21 12 1...
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