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GO Classes DPP | GATE DA | Probability | Discrete Random Variables

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We use $Var(X)=E(X^2)-[E(X)]^2$.

First,
$E(X)=\sum xP(X=x)$

$E(X)=0(0.2)+1(0.4)+2(0.3)+3(0.1)$

$E(X)=0+0.4+0.6+0.3=1.3$

Next,
$E(X^2)=\sum x^2P(X=x)$

$E(X^2)=0^2(0.2)+1^2(0.4)+2^2(0.3)+3^2(0.1)$

$E(X^2)=0+0.4+1.2+0.9=2.5$

Therefore,
$Var(X)=2.5-(1.3)^2$

$Var(X)=2.5-1.69=0.81$

So, the variance is $\boxed{0.810}$.

Correct option: C

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