36 votes 36 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 $R=0$ $R<0$ $R\geq 0$ $R > 0$ Probability gatecse-2011 probability random-variable expectation normal + – go_editor asked Sep 29, 2014 • edited Dec 4, 2017 by pavan singh go_editor 8.9k views answer comment Share Follow See all 3 Comments See all 3 3 Comments reply Anand. commented May 25, 2018 reply Follow Share Catch is that Variance can never be negative. 6 votes 6 votes Divy Kala commented Nov 21, 2018 reply Follow Share Unless we are dealing with numbers with imaginary parts! 0 votes 0 votes Abhishek Rauthan commented Dec 31, 2022 reply Follow Share The variance of a random variable X is defined to be Var(X) = E [(X − E [X])]^2 = E[X^2] − E [X] ^2The variance is always nonnegative since we take the expectation of a nonnegative random variable (X − E [X])^2source https://web.stanford.edu/class/archive/cs/cs109/cs109.1218/files/student_drive/3.3.pdf see definition 3.3.1 0 votes 0 votes Please log in or register to add a comment.
Best answer 36 votes 36 votes 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. Regina Phalange answered Apr 26, 2017 • edited Oct 30, 2018 by Mk Utkarsh Regina Phalange comment Share Follow See 1 comment See all 1 1 comment reply Mayank0343 commented Jun 22, 2019 reply Follow Share 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. 0 votes 0 votes Please log in or register to add a comment.
16 votes 16 votes answer is option c . Lone Wolf answered Dec 13, 2018 Lone Wolf comment Share Follow See all 0 reply Please log in or register to add a comment.
13 votes 13 votes V(x) = E(x^2) - [E(x)]2 = R where V(x) is the Variance of x, Since Variance is Square and Hence Never be Neagtive, R>=0 aman.anand answered Dec 29, 2016 aman.anand comment Share Follow See all 0 reply Please log in or register to add a comment.
2 votes 2 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/ Ram Swaroop answered Feb 20, 2019 Ram Swaroop comment Share Follow See all 0 reply Please log in or register to add a comment.