# Expected value

1. May 13, 2013

### ParisSpart

we have variables X,Y with f(m,n)=P(X=m,Y=n) with f(0.1)=0.1 f(1.0)=0.1 f(1.1)=0.344
find the expectation value E(X+Y)

i need help because i dont how to start to solve this , if i begin with the definition of the expected value i cant do anything any ideas?

2. May 13, 2013

If your function f requires two arguments, as you indicate by f(m,n), how can you calculate f(0.1) = 0.1 and so on? do you mean f(0,1) = 0.1, f(1,0) = 0.1, f(1,1) = 0.344?
What values other than 0 and 1 are possible for X and Y, or are these the only possibilities? Make sure you've provided ALL the information accurately.

3. May 13, 2013

### ParisSpart

f(m.n) the m and n takes 0 and 1 values ...

4. May 13, 2013

I will assume my comment about you meaning f(0,1) instead of f(0.1) was correct.
Think about it this way: if X, Y can each be only 0 or 1 there are only 4 possibilities: (0,0), (1,0), (0,1), (1,1). You have the probabilities assigned to three of the four, so you can make a table with two columns (labeled 0 and 1) and two rows (also labeled 0 and 1). In each cell put the appropriate probability:
In cell (0,1) put .1, in cell (1,0) put .1, in cell (1,1) put 0.344. (Since the four probabilities have to sum to 1 you can find the probability for cell (0,0) yourself.)

Now you have two ways to go.
Method A: To calculate the expectation work out the sum

$$E(X+Y) = \sum f(m,n) (m+n)$$

- it will have as many terms as there are cells in the table.

Method B:
The rows of your table have the values for X, the columns the values for Y, so the edges of the table give the marginal distributions of X and Y. Then

$$E(X+Y) = E(X) + E(Y)$$

can be calculated using the appropriate marginal distributions.

Methods A and B give the same answer (when applied correctly) so you can use whichever you prefer.

Set things up and try the work before posting more questions.

Last edited: May 13, 2013
5. May 13, 2013

### ParisSpart

i dont understand the commands of the table.... the commands...

6. May 13, 2013

### ParisSpart

can you write again the table?

7. May 13, 2013

### Ray Vickson

More important: can YOU write the table? If so, do it. If you cannot, tell us why.

8. May 13, 2013

### ParisSpart

if i wanted to find the P(X=0) i will find f(0,0) and if yes , why?