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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. $R > 0$

Catch is that Variance can never be negative.
Unless we are dealing with numbers with imaginary parts!

The difference between  $(E[X²])$ 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.

### 1 comment

I totally agree with the answer. However the term used here is difference. does it not mean it could be mean^2-m.s.v as well.

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

This the definition definition of variance .  Variance never be negative.Variance is the average squared deviation from the mean. Notice the word “squared”. It may be zero.  Variance of constant is zero.Theorem 2 a