Originally Posted by

**hasbren** Here's the question:

Let x1,x2,x3 be a random sample from a distribution with a PDF: f(x) = 2x, 0<x<1.

a) find the probability that the largest of x1,x2,x3 is less than the distribution median.

b) Find Cov(x(2),x(3))

Using quantiles, I found the distribution median to be = sqrt(1/2);

I found the max to be the pdf 6x^5 0<x<1;

In order to solve this, P(6x^5 < sqrt(1/2)) solved for x. This gave me an integral 2x with bounds from 0 to (((sqrt(.5))/6))^(1/5)) yielding 0.42514

Did I go through this correctly?

For the Covariance I am also not confident.

using the definition that cov(x,y) = E[(x - E(x))(Y - E(y))]

I found to be something like E[(12x^3-12x^5-24/35)(6x^5-6/7)] which I calculated to be around 78/245.

Thanks in advance for you help!