Question

The following table shows the probability of rolling the numbers 1 through 7

on a fair 7-sided die.
х
1
2
3
4
5
6
7
P(X) 1/71/71/71/71/71/71/7
What is the standard deviation of the random variable X, "the number that
comes up on the die"?
A. 1.708
OB. 3.745
O C. 2.917
Оооо
D. 3.5
E. 2.0

Answer 1

2.0

Explanation:

Couldn't really understnd what you wrote but I'll assume it's the standard deviation of a fair, 7-sided die

The standard deviation is just the square root of the variance (which is just the second moment minus the first moment squared)

The first moment (AKA the average is..)

`(1+2+3+4+5+6+7)/(7)=4`

The second moment is..

`(1^2+2^2+3^2+4^2+5^2+6^2+7^2)/(7)=20`

`√(20-4^2)=2`