Question

Let X be a random variable taking values x₁, x₂,..., x_n with probabilities p₁, p₂, ..., p_n, respectively. Then var(X) = ______.

Answer 1

Let X be a random variable taking values x₁, x₂,..., x_n with probabilities p₁, p₂, ..., p_n, 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`