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+17 votes

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. $R > 0$
asked in Probability by Veteran (103k points)
edited by | 1.4k views

This might help ....

Catch is that Variance can never be negative.

3 Answers

+14 votes
Best answer

Answer is (C).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.

answered by Loyal (8.5k points)
edited by
+10 votes

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

answered by Junior (565 points)
+5 votes
answer - C
answered by Loyal (9k points)

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