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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. $R > 0$
asked in Probability by Veteran (96.1k points)
edited by | 2.2k views
+8

This might help ....

0
Catch is that Variance can never be negative.
0
Unless we are dealing with numbers with imaginary parts!

5 Answers

+17 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 (9.3k 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 (609 points)
+5 votes
answer - C
answered by Loyal (8.7k points)
+3 votes

answer is option c .

answered by Active (1.4k points)
0 votes
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

Answer C

https://www.macroption.com/can-variance-be-negative/

answered by Active (3k points)
Answer:

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