# Can someone Please help me understand E(X) expected values in statistics

## Homework Statement

I have two dice, let X and Y denote (rspectively) min and maximum of the number of spots showing on the two die. Determine E(Y|X=x) for 1 <= x <=6.

## Homework Equations

Basically all I need to do is work out E(Y| x=1), E(Y|x=2) and so on until x=6. The reason I am stuck is that the teacher has told me that E(Y|X=1)=1 and I don't understand how.

## The Attempt at a Solution

I was thinking that E(Y|X=2) so that means (I think) that when X=2 that is the maximum, so then I thought Y could either be 1 or 2, so that means 2/36 ? But how come E(Y|X=1) is =1?

See the problem is, statistics is the only branch of mathematics I don't enjoy so I can't really get my head around the question and what it's asking

## Answers and Replies

I don't understand what you mean by the "min and maximum of the number of spots showing on two die". A die has a fixed number of spots so how can there be a minimum and maximum?

nicksauce
Science Advisor
Homework Helper
Do you mean to say that X is the maximum and Y is the minimum? Because it does not make any sense that E(Y|X=1) = 1 otherwise.

Suppose that that's what you mean. Then X = 1 implies Max{Die1,Die2} = 1. Clearly this is only possible in the case where Die1 and Die2 are both equal to 1, hence E(Y|X=1) = 1, as it's the only value Y can have.

Think of it like this. You roll one die. It comes up, say, 4. Then you roll a 4-sided die. What's your expected value now? This is how conditional expectation works. So, E[Min | Max=4] = 1/4*(1+2+3+4) = 2.5.

Say you have two die $$D_1$$ and $$D_2$$. If one of them comes up as 1 and the other comes up as $$n$$ then $$min{D_1,D_2}$$ is always going to be 1. This is because the minimum of 1 and any other number has to be 1 because you can't roll lower than 1!