Question

Consider a fair of six-sided of die is rolled. Let x be a number of uppermost face. What is the variance of x?

Answer 1

Using the uniform distribution, it is found that the variance of x is of 2.0833.

What is the uniform probability distribution?

It is a distribution with two bounds, a and b, in which each outcome is equally as likely.

The variance is given by:

$V(X) = \frac{(b - a)^2}{12}$

In the die, all outcomes between 1 and 6 are equally as likely, hence the bounds are a = 1, b = 6, and the variance is given by:

$V(X) = \frac{(6 - 1)^2}{12} = 2.0833$

More can be learned about the uniform distribution at brainly.com/question/13889040