Unformatted text preview: X iX j ) f x ( j ) ( X j ) = f x ( ij ) ( X iX j ) f x ( j ) ( X j ) = 2 i e2 X i ( X iX j ) ij1 X j1 j ( ij1)!( j1)! ,X i > X j > 0. 3df. y ( n ) = 1 with prob. p n ; y ( n ) = 0 with prob. 1p n . 3d. LIM n →∞ Pr [  y ( n ) > ² ] = LIM n →∞ Pr [ y ( n ) = 1] = LIM n →∞ p n = 0. 3e. LIM n →∞ E [( y ( n )0) 2 ] = LIM n →∞ 1 2 · Pr [ y ( n ) = 1] = LIM n →∞ 1 2 p n = 0. 3f. LIM n →∞ ∑ n i =1 Pr [  y ( i ) > ² ] = LIM n →∞ ∑ n i =1 Pr [ y ( n ) = 1] = LIM n →∞ ∑ n i =1 p i = ∑ ∞ i =1 p i = p 1p < ∞ → converge with prob. 1....
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 Spring '10
 Lehman

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