00:02
All right, so in this question, we have variables x1, xn, which are uniform over the interval 0, 1, right? so remember that a uniform distribution is f of x1 is less than or equal to x, so the cdf of it is going to be equal to x.
00:22
All right, this should make sense to you.
00:23
When you differentiate this, you just get 1, which is the pdf.
00:28
And y is the max of x1 to xn.
00:33
So the classic way to say this is the cdf of y, so i don't know why i wrote this like this, we'll write it as p.
00:39
The cdf, the probability that y is less than or equal to y, is just to say that the probability, this is just the probability that all of the x of i are less than, right? so this is like the product of the probability that x of i is less than or equal to y for all of these.
00:57
And this is just y to the n, right? so then we just go, that's the cdf right there.
01:05
We just got to the cdf.
01:07
And again, this is only going to be value for y and 0, 1.
01:12
You can, right, for greater than 1, it's going to just be, the cdf should just be equal to 1, and for less than 0, it should just be 0.
01:18
And the pdf is just, we differentiate this, right? so we say the pdf of y is just the derivative of this, is vector y...