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Question
Let X be a random variable taking values x1, x2,..., xn with probabilities p1, p2, ..., pn, respectively. Then var(X) = ______.
Solution
Let X be a random variable taking values x1, x2,..., xn with probabilities p1, p2, ..., pn, respectively. Then var(X) = `sum"p"_"i""x"_"i"^2 - (sum"p"_"i"x_"i")^2`.
Explanation:
Var(X) =E(X2) – [E(X)]2
= `sum"X"^2"P"("X") - [sum"X"."P"("X")]^2`
= `sum"p"_"i"x_"i"^2 - (sum"p"_"i"x_"i")^2`
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