If X be a random variable taking values ${x_1},{x_2},{x_3}, \ldots ,{x_n}$ with probabilities ${{\rm{P}}_1},{{\rm{P}}_2},{{\rm{P}}_3}, \ldots ,{{\rm{P}}_{\rm{n}}}$, respectively. Then, Var$(x)$ is equal to…………….
If X be a random variable taking values ${x_1},{x_2},{x_3}, \ldots ,{x_n}$ with probabilities ${{\rm{P}}_1},{{\rm{P}}_2},{{\rm{P}}_3}, \ldots ,{{\rm{P}}_{\rm{n}}}$, respectively. Then, Var$(x)$ is equal to…………….
Official Solution
VVidaara Team
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${\mathop{\rm Var}\nolimits} (X) = E{(X)^2} - {[E(X)]^2}$
$= \sum\limits_{i = 1}^n {{X^2}} P(X) - {\left[ {\sum\limits_{i = 1}^n X P(X)} \right]^2}$
$= \sum {{P_i}} x_i^2 - {\left( {\Sigma {P_i}{x_i}} \right)^2}$
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