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If the difference between the expectation of the square of a random variable $\left(E\left[X^2\right]\right)$ and the square of the expectation of the random variable $\left(E\left[X\right]\right)^2$ is denoted by $R$, then

  1. $R=0$
  2. $R<0$
  3. $R\geq 0$
  4. $R > 0$
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Answer is (C).
The difference between  $(E[X^2])$ and $(E[X])^{2}$ is called variance of a random variable. Variance measures how far a set of numbers is spread out. (A variance of zero indicates that all the values are identical.) A non-zero variance is always positive.

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V(x) = E(x^2) - [E(x)]= R

where V(x) is the Variance of x, Since Variance is Square and Hence Never be Neagtive, R>=0

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