Question

X 1 2 3 4 5 6 7 8
P(X) 1/8 1/8 1/8 1/8 1/8 1/8 1/8 1/8

What is the standard deviation of the random variable X, "the number that comes up on the die"?

A. 3.745
B. 3.5
C. 1.708
D. 14.028
E. 2.291

Answer 1

The variance for the distribution is given by
\[\mathbb E(X^2)-\mathbb E(X)^2=\sum_x x^2p(x)-\left(\sum_xxp(x)\right)^2\]and the standard deviation is the square root of the variance.