There are 10 balls in an urn, numbered from 1 to 10. if 5 balls are selected at random and their numbers are added, what is the expected value of the total?

Let denote the value on the -th drawn ball. We want to find the expectation of , which by linearity of expectation is

(which is true regardless of whether the are independent!)

At any point, the value on any drawn ball is uniformly distributed between the integers from 1 to 10, so that each value has a 1/10 probability of getting drawn, i.e.

and so

Then the expected value of the total is

i think the answer is b x = 1, y = 35/2