# Probability Distribution and Density help

1. Oct 8, 2006

### Leper Messiah

I have some homework that I must do, and I have figured out about half of it, but the other half is a complete mystery. I understand the theorems tied to these problems, but cannot do them for some reason or another.

Probability distribution for RV X is given by
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. Help with any of them would be much appreciated. Thank you very, very much!!!

Last edited: Oct 8, 2006