Solutions_Assignment4 11-24'

Solutions_Assignment4 11-24' - EEE554 Assignment 4 Solution...

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EEE554 Assignment 4, Solution of problem (11.24) (11.24) Determine E [(2 X + 1) 2 ] for a N ( μ, σ 2 ) random variable. E [(2 X + 1) 2 ] = E [(2 X + 1)(2 X + 1)] = E [4 X 2 + 4 X + 1] = 4 E [ X 2 ] + 4 E [ X ] + 1 using linearity of expectation operator = 4 E [ X 2 ] + 4 μ + 1 . As variance is deFned as σ 2 = E [ X 2 ] - ( E [ X ]) 2 = E [ X 2 ] - μ 2 , we can express
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