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  • Fill in the blanks in the following question: Let X be a random variable taking values x1, x2,..., xn with probabilities p1, p2, ..., pn, respectively. Then var (X) =

Fill in the blanks in the following question:
Let X be a random variable taking values x1, x2,..., xn with probabilities p1, p2, ..., pn, respectively. Then var (X) =

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Solution

\\\operatorname{var}(\mathrm{X})=\mathrm{E}\left(\mathrm{X}^{2}\right)-[\mathrm{E}(\mathrm{X})]^{2}, where \ \mathrm{E}(\mathrm{X})\ represents \ mean \ or \ expected \ value \ for \ random \ variable \ \mathrm{X}
Variance is the mean of deviation of Random variable from its expected value. \operatorname{Var}(X)=\sum_{D i}\left(X_{i}-X\right)^{2}
On expanding we get the formula: \operatorname{var}(\mathrm{X})=\mathrm{E}\left(\mathrm{X}^{2}\right)-[\mathrm{E}(\mathrm{X})]^{2}

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