A fair die is thrown. What is the variance of its score?

\frac{35}{12}

Correct answerYour answer

\frac{7}{2}

Correct answerYour answer

\frac{35}{6}

Correct answerYour answer

\frac{91}{6}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

$E(X) = \frac{7}{2}$ and $E(X^{2}) = \frac{1 + 4 + 9 + 16 + 25 + 36}{6} = \frac{91}{6}$ .
$\text{Var}(X) = \frac{91}{6} - \frac{49}{4} = \frac{182 - 147}{12} = \frac{35}{12}$ .

Worth noting

$\frac{91}{6}$ is $E(X^{2})$ before the square of the mean is taken away.

Ten questions from Random Variables, Expectation & Variance, at your own pace.

Ten questions from Random Variables, Expectation & Variance, at your own pace.

Explanation