What is the expected value of minimum of i.i.d random variables that are drawn from U(0,1) distribution

Let are the random variables.

Let

Plan of Action

- Find CDF for X
- Find PDF for X using CDF
- Compute

Note that

Thus

so

Alternative way :

For non-negative random variables, some times it is easy to calculate expected value of random variable using following formula :

Since in our case cannot take value greater than 1