Probability - Sum of Squares of Rolls of a Die

[jchiz24]

Homework Statement

Roll a fair die n times. Let Sn denote the sum of squares of the rolls. Thus, Sn is the sum of Xi^2, where Xi represents one roll.

What are the mean and variance of sqrt(n) * (Sn/n - u), where u is the mean of Yn/n

Homework Equations

The Attempt at a Solution

No real revelation yet, but looking into law of large numbers. Not sure if should pursue problem directly via definition of expected value and variance...

 

[statdad]

Homework Statement

Roll a fair die n times. Let Sn denote the sum of squares of the rolls. Thus, Sn is the sum of Xi^2, where Xi represents one roll.

What are the mean and variance of sqrt(n) * (Sn/n - u), where u is the mean of Yn/n

Homework Equations

The Attempt at a Solution

No real revelation yet, but looking into law of large numbers. Not sure if should pursue problem directly via definition of expected value and variance...

So you are calling the results of individual rolls X_i, and

<br /> S_n = X_1^2 + X_2^2 + \cdots X_n^2<br />

You give the definition that u is the mean of

<br /> \frac{Y_n}{n}<br />

What is Y_n?