# Expectation of X

• Oct 4th 2009, 10:35 AM
dude15129
Expectation of X
I am working on this problem and I don't really know what to do. I am really struggling in this class.

A bag contains n balls numbered 1, 2, 3, ....n. Two of them are taken out of the bag (without replacement). Let X be the maximum value among the two selected balls.

(a) Find the mean E(X) when n=5.
(b) Generalize to any n.

I know the formula for Expectation is ∑xP(X=x)

I just don't know what to do.
Thanks for any help.
• Oct 4th 2009, 12:55 PM
novice
Quote:

Originally Posted by dude15129
I am working on this problem and I don't really know what to do. I am really struggling in this class.

A bag contains n balls numbered 1, 2, 3, ....n. Two of them are taken out of the bag (without replacement). Let X be the maximum value among the two selected balls.

(a) Find the mean E(X) when n=5.
(b) Generalize to any n.

I know the formula for Expectation is ∑xP(X=x)

I just don't know what to do.
Thanks for any help.

Since you know the formula, you are very close to it, and I don't want to spoil the fun. I will give the hint.

Your x's are already been stated in the question. First know what exactly is in you sample space, S. Knowing your x's and S, you should know your P(X=x).

If you know part (a), you will know part (b) by experimenting n=1, 2, 3.

From n=1 to 3, you should see the pattern, then express it using ∑ for the range from 1 to n.
• Oct 4th 2009, 01:47 PM
Plato
Quote:

Originally Posted by dude15129
A bag contains n balls numbered 1, 2, 3, ....n. Two of them are taken out of the bag (without replacement). Let X be the maximum value among the two selected balls.
(a) Find the mean E(X) when n=5.
(b) Generalize to any n.

There are only $\binom{5}{2}=10$ ways to choose 2 items from 5.
You can easily list them out $\{ 1,2\} ,\{ 1,3\} ,\{ 1,4\} ,\{ 1,5\} ,\{ 2,3\} , \cdots \{ 4,5\}$.
From which you can see $X=1,2,3,4$ and $P(X=4)=\frac{1}{10}$.

Now you finish.