f(x) = { 1/5 for 2 < x < 7; 0 elsewhere

find P(3 < X < 5) as a fraction.

also,

Show that f(x) = 3x^2 for 0 < x < 1

find P(0.1 < X < 0.5) as a decimal

also,

Probability density for RV Y is given by

f(y) = { 1/8(y+1) for 2 < x < 4; 0 elsewhere

find P(Y < 3.2) and P(2.9 < 3.2) to four decimal places

also,

find value of k for:

f(z) = {kze^-z^2 for z > 0; 0 for z <= 0

also,

find P(X < 1/4) and P(X > 1/2) for

g(x) = {6x(1-x) for 0 < x < 1; 0 elsewhere

I really understand that this is a lot, but I honestly need help with these, and I have no idea how to answer them at all. Thank you very, very much!!!