Let and ^2 denote the mean and variance of the random variable X..pdf

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Let ? and ?^2 denote the mean and variance of the random variable X. Determine E[((X-?))/?] and E{[((X-?))/?]^2 } and support your answers. Solution u, are known constants E[ (x-u)/ ] = E [ (x/) - (u/) ] = E[ x/ ] - u/ = (1/) * E[x] - u/ = (1/)*u - u/ = 0 E [ ((x-u)/)2 ] = (1/2 ) * E [ X2 + u2 - 2*x*u ] = (1/2 ) * ( E [ X2 ] + u2 - 2*E[x]*u ) = (1/2 ) * ( E [ X2 ] + u2 - 2*u2 ) = (1/2 ) * ( E [ X2 ] - u2 ) (now 2 = E[x2 ] - u2) = (1/2 ) * 2 = 1.

$Let ? and ?^2 denote the mean and variance of the random variable X. Determine E[((X-?))/?] and E{[((X-?))/?]^2 } and support your answers. Solution u, are known constants E[ (x-u)/ ] = E [ (x/) - (u/) ] = E[ x/ ] - u/ = (1/) * E[x] - u/ = (1/)*u - u/ = 0 E [ ((x-u)/)2 ] = (1/2 ) * E [ X2 + u2 - 2*x*u ] = (1/2 ) * ( E [ X2 ] + u2 - 2*E[x]*u ) = (1/2 ) * ( E [ X2 ] + u2 - 2*u2 ) = (1/2 ) * ( E [ X2 ] - u2 ) (now 2 = E[x2 ] - u2) = (1/2 ) * 2 = 1$

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1. Let ? and ?^2 denote the mean and variance of the random variable X. Determine E[((X-?))/?] and E{[((X-?))/?]^2 } and support your answers. Solution u, are known constants E[ (x-u)/ ] = E [ (x/) - (u/) ] = E[ x/ ] - u/ = (1/) * E[x] - u/ = (1/)*u - u/ = 0 E [ ((x-u)/)2 ] = (1/2 ) * E [ X2 + u2 - 2*x*u ] = (1/2 ) * ( E [ X2 ] + u2 - 2*E[x]*u ) = (1/2 ) * ( E [ X2 ] + u2 - 2*u2 ) = (1/2 ) * ( E [ X2 ] - u2 ) (now 2 = E[x2 ] - u2) = (1/2 ) * 2 = 1