Let u1, un be i.i.d. unif(0, 1), and x = max(u1, un). what is the pdf of x? what is ex? hint: find the cdf of x first, by translating the event x < x into an event involving .

Step-by-step explanation:

A uniform distribution, "sometimes also known as a rectangular distribution, is a distribution that has constant probability".

We need to take in count that our random variable just take values between 0 and 1 since is uniform distribution (0,1). The maximum of the finite set of elements in (0,1) needs to be present in (0,1).

If we select a value we want this:

And we can express this like that:

for each possible i

We assume that the random variable are independent and from the definition of an uniform random variable between 0 and 1. So we can find the cumulative distribution like this:

And then cumulative distribution would be expressed like this:

For each value we can find the dendity function like this:

So then we have the pdf defined, and given by:

 and 0 for other case

And now we can find the expected value for the random variable X like this: