# Breaking down a summation

1. Mar 22, 2008

### Somefantastik

Can someone help me break this down?

$$\Sigma^{k}_{i=1}\frac{i \left(^{n}_{i}\right)\left(^{m}_{k-i}\right)}{\left(^{m+n}_{k}\right)}$$

2. Apr 4, 2008

k*n/(m+n)

3. Apr 4, 2008

### Somefantastik

Thanks for your help, but I had the answer and was really looking for the process.

4. Apr 5, 2008

### ssd

Look at the expectation of a Hypergeometric variable.

5. Apr 9, 2008

First translate from math to English: there are m red balls and n blue balls in a sack from which you randomly draw k balls. What is the expected number of blue balls drawn? Now translate back into math: try using indicator random variables $X_{j}$ which equal 1 if the j-th drawn ball is blue and 0 if it is red. Now define the random variable
$$X = \sum_{j=1}^{k} X_{j}$$