1. ## Statistics

There are four boxes where each box contains nine balls with the number 0 on them and one ball with the number 3 on it. Given that one ball is taken out from each box, determine the mean and standard deviation of the average of the four numbers.

[Sol] Letting X be the number of balls chosen with the number 3 on them, and Y be the average of the four numbers.

$Y= \frac{3X + 0\cdot (4-X)}{4}$

A few questions.

Why is Y set up like that? How is it derived?

Where is 4-X derived?

Why is Y, set up like that, the average of the 4 numbers?

In the formula $\mu _Y = a \cdot \mu _X + b$, what are a and b?

2. Originally Posted by chengbin
There are four boxes where each box contains nine balls with the number 0 on them and one ball with the number 3 on it. Given that one ball is taken out from each box, determine the mean and standard deviation of the average of the four numbers.

[Sol] Letting X be the number of balls chosen with the number 3 on them, and Y be the average of the four numbers.

$Y= \frac{3X + 0\cdot (4-X)}{4}$

A few questions.

Why is Y set up like that? How is it derived?

Where is 4-X derived?

Why is Y, set up like that, the average of the 4 numbers?

In the formula $\mu _Y = a \cdot \mu _X + b$, what are a and b?
If X balls have the number 3 on them then 4 - X balls have the number zero on them. The total score is (number of balls with 3 on them)(3) + (number of balls with zero on them)(0) = (X)(3) + (4 - X)(0). Divide by the number of balls (4) to get the average.