Which of the following is not true for a random variable X that is uniformly distributed over the interval $a \leq x \leq b$ ?
A)E(X) = (a + b)/2.
B)V(X) = $( b - a ) ^ { 2 }$ /12.
C) $\sigma$ = (b - a)/6.
D) $f ( x ) = 1 / ( b - a )$ if a $\le$ x $\le$ b.

Question

Which of the following is not true for a random variable X that is uniformly distributed over the interval $a \leq x \leq b$ ?
A)E(X) = (a + b)/2.
B)V(X) = $( b - a ) ^ { 2 }$ /12.
C) $\sigma$ = (b - a)/6.
D) $f ( x ) = 1 / ( b - a )$ if a $\le$  x $\le$  b.

Quizplus · Accepted Answer

C) is not true because the correct formula for the standard deviation ($\sigma$) of a uniform distribution is $\sigma = \sqrt{(b - a)^2 / 12}$, not $(b - a)/6$.

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