Let f(x) = k(3x - x^2) if x is between 0 and 3 (includes 0 and includes 3), and f(x) = 0 if x is less than 0 or greater than 3 (does not include 0 and does not include 3)

a). For what value of k is f a probability density function?
b). For that value of k, find P(X>1)
c). Find the mean


I need as much help as I can get on this problem! If you scratch my back, I will scratch yours

So, thanks in advanced in reading and I hope someone can help me!

Need to complete this by 2moro

iirc probability density functions have an area of 1. so integrate your function, set it equal to 1, and solve for k

for b, since the area under the curve is the probability, find the area where x > 1

This post was edited by carteblanche on Apr 8 2015 07:51pm

for a) u want integral to be equal to 1
int(x= 0 to 3) k(3x - x^2) dx = 1
solve for k and get k=2/9

for use k u just found and integrate from 1 to 3 to get 20/27

for c) int (x=0 to 3) xf(x) dx = 3/2

Thanks for the help guys!

I will take your advice and if I have any questions along the way I will post them here!

But for now I should be good!