The diameter of sand grains in a special sand roof, measured in mm, can be considered as a random variable X with probability density:

f(x)={k(xx4)0..

Determine the constant k so that this becomes a valid probability density.

Find the expectation E (X) and the variance V (X).

Find the expectation E (4X + 3) and the variance V (4X + 3).

I need some help understanding probability density and how to use the equation. If you could answer these questions in detail it would be greatly appreciated :)