InterviewSolution
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InterviewSolution
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Find the variance and standard deviation of the random variable X whose probability distribution is given below : `{:(x,0,1,2,3),(P(X=x),1/8,3/8,3/8,1/8):}` |
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Answer» ` E(X) = sum p_(i) x_(i) ` ` = 1/8 xx 0 + 3/8 xx 1 + 3/8 xx 2 + 1/8 xx 3` ` = 3/8 + 6/8 + 3/8 = 12/8 = 3/2` ` E(X^(2)) = sum p_(i)x_(i)^(2)` ` - 1/8 xx 0^(2) + 3/8 xx 1^(2) + 3/8 xx 2^(2) + 1/8 xx 3^(2) ` ` = 0 + 3/8 + 12/8 + 9/8 = 24/8 = 3` Var (X) = `E (X^(2)) - [E(X)]^(2)` ` = 3 - (3/2)^(2)` ` = 3 - 9/4 = (12 - 9)/4 = 3/4 ` Standard deviation, `sigma = sqrt("Var(X)") = sqrt(3/4)` `sigma = sqrt3/2` ` :. " " Var (X) = 3/4 , sigma = sqrt3/2` |
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