Let (x, y) be a uniformly random point in the triangle in the plane with vertices (0,0), (0, , 0). find cov(x, y ) and corr(x, y ).

Denote the triangle by , so that

We have

(Alternatively, is a triangle with base and height 1, so its area is 1/2.)

Then the joint PDF of is

Covariance is defined as

We can get the expectations we need from the joint PDF:

Then the covariance is

Correlation is defined as

We have for any random variable ,

Now,

so that the correlation is

i'm pretty sure it's c. nvm

b. 24 mm

step-by-step explanation:

use the pythagorean theorem.

a^2 + b^2 = c^2

a^2 + 7^2 = 25^2

a^2 + 49 = 625

a^2 = 576

a = 24

answer: b. 24 mm