If X1,X2, . . . ,Xn are independent U(0, 1) random variables and Y=min (X1,X2, . . . ,Xn) has PDF given by
fY(x) = { , 0<=x<=1}, 0, otherwise
Identify this distribution, and hence state E[Y] and Var(Y).
Im thinkin it looks similar to a binomial distribution? Am i on the right lines?
minimum of X1,...,Xn is the smallest of these rvs
It's also known as the smallest order stat.
It couldn't be a binomial since the underlying distribution here is continuous (uniform)
for any 0<a<1
So
THIS is a Beta with parameters 1 and n.
Look that up for your mean and variance.
The min business is irrelevant (unless you want to derive the given pdf). The bottom line is that you're given a pdf and asked to identify it and hence get it's mean and variance. Note that you can check your answers by calculating the mean and variance directly from the pdf.