Urgent Help - Continuous Random Variables

The random variable f(x) is given by f(x) = kx(16-x^2) for 0<_x<_4


a) find the value of k.

b) find F(X)

The random variable f(x) is given by f(x) = kx(16-x^2) for 0<_x<_4


a) find the value of k.

b) find F(X)

Show some working, this is a pretty standard question in terms of method.

Also, for (b), do you mean find E(X)?

No it is F(x)

The method is to integrate f(x) and put in the 4 and 0 as x. Then take it away, but I keep getting the wrong answer.

16kx - kx^2 = 1

integrated = 8kx^2 - kx^3/3 =1

8k x 4^2 - k x 4^3 / 3 - 8k x 0 - k x 0/3 =1

128k - 64/3k = 1

And then you get some dodgy answer for k.

It's because the integration is

$\displaystyle\int 16kx-kx^3dx$

I think you made an error in the first line

_Kar.

f(x) = kx(16-x^2) for 0<_x<_4

What did u get when u multiplied out the brackets ?

I got 16kx - kx^2

$kx(16-x^2) =[br][br]kx\times16 - kx\times x^2= [br][br]16kx - kx^3$

_Kar.

**** sakes I made the silliest mistake, which wasted 30mins of my life.

But thanks m8, for helping me out.

The random variable f(x) is given by f(x) = kx(16-x^2) for 0<_x<_4


a) find the value of k.

b) find F(X)