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## Homework Statement

Suppose that 15 observations are chosen at random for the pdf f(Y) = 3y^2 on the interval 0 to 1. Let X denote the number that lie in the interval (.5,1). Find E(X)

## Homework Equations

## The Attempt at a Solution

Ok so to get the expected value u integrate the pdf times the random variable.

Doing this is the integral 3y^3 and it turns to .75y^4

This is where I get confused. First of all I thought that it would have summed to 1 so that the number of X on that range would be 15, but it can't be it would be 11.25

Aside from that, to find the number over this range i kno is 15x the expected value but i can't figure out the bounds. Is it the value of 0,1 - the value of .5,1 or something else all together

Thanks in advance