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Unformatted text preview: (a) (2.5 pts) E [ X ] , Answer : Remember that @M X ( t ) @t & & & t =0 = E [ X ] : Then, @ @t ± 1 (1 & ²t ) ² = ³ & (1 & ²t ) & 2 ( & ² ) ´ = ² (1 & ²t ) 2 and @M X ( t ) @t & & & t =0 = E [ X ] = ²: 1 (b) (2.5 pts) E [ X 2 ] : Answer : Remember that @ 2 M X ( t ) @t 2 & & & t =0 = E [ X 2 ] : Then, @ 2 @t 2 ± 1 (1 & &t ) ² = @ @t ± & (1 & &t ) 2 ² = & 2 & (1 & &t ) & 3 ( & & ) = 2 & 2 (1 & &t ) 3 and @ 2 M X ( t ) @t 2 & & & t =0 = E [ X 2 ] = 2 & 2 : 2...
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 Spring '11
 zobuz

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