X takes the values -1, 0 and 1 with probabilities 1/4, 1/2 and 1/4. What is the standard deviation of X?

Question 58

MediumOriginal question

$X$ takes the values $-1$ , 0 and 1 with probabilities $\frac{1}{4}$ , $\frac{1}{2}$ and $\frac{1}{4}$ . What is the standard deviation of $X$ ?

0

Correct answerYour answer

\frac{1}{2}

Correct answerYour answer

\frac{\sqrt{2}}{2}

Correct answerYour answer

1

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

$E(X) = -\frac{1}{4} + 0 + \frac{1}{4} = 0$ and $E(X^{2}) = \frac{1}{4} + 0 + \frac{1}{4} = \frac{1}{2}$ .
$\text{Var}(X) = \frac{1}{2}$ , so the standard deviation is $\sqrt{\frac{1}{2}} = \frac{1}{\sqrt{2}}$ .

Worth noting

$\frac{1}{2}$ is the variance; the standard deviation is its square root.

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