Multiple choice

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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C Correct answer
Explanation

R = E[X²] - (E[X])² is the definition of variance, which is always non-negative because variance measures spread and cannot be negative. R = 0 only when the random variable is constant. R > 0 when the variable has any variation. Therefore R >= 0 is always true.

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