Probability

Concept:If a random variable takes only one value (constant), its spread is zero.Explanation:Let the random variable $X$ be constant, i.e., $X = c$ for all outcomes.Then the expected value $E[X] = c$, which may or may not be zero. So option A is wrong.The variance is $Var(X) = E[(X - c)^2] = 0$, so the standard deviation $\sqrt{Var(X)} = 0$.Thus, the standard deviation is zero, not positive. So option C is wrong.Zero is a real number, but option D is vague; the specific correct statement is that the standard deviation is zero.Answer:Option B is correct.