Let X be a random variable with the following probability distribution: x 1 2 3 4 P(X) 0.4 0.3 0.2 0.1 Find the expected value and variance.

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$E (X) = 1 (0.4) + 2 (0.3) + 3 (0.2) + 4 (0.1) = 2$

$E(X^2)=1^2(0.4)+2^2(0.3)+3^2(0.2)+4^2(0.1)=5$

$Var(X)=\sigma^2=E(X^2)-(E(X))^2=5-(2)^2=1$

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