# Using a probability density function.

• Jun 30th 2010, 05:11 AM
laurenng
Using a probability density function.
I've never had a problem figuring out a problem before, and if I can't solve it I usually take the zero on that problem.

But this is a group work assignment and we have to each do a problem from a section that wasn't lectured on. If any one person doesn't have their section he won't accept any part from the group...

So of course I'm COMPLETELY lost.

In case it helps, I'm using "Calculus - Volume 2" by James Stewart. (It's one Calc book split into three smaller ones used at the University of Florida.) It's published by Thomson. The problem I have to do is section 8.5, number 6.

Let f(x)=kx^2 if 0<x<1 (these symbols should also have 'or equal to') and f(x)=0 if x<0 or x>1
a) For what value of k is f a probability density function?
b) For that value of k, find P(X>1/2) ('or equal to').
c) Find the mean.

Let me know if there's any other information you need to help me out. Thanks!
• Jun 30th 2010, 06:18 AM
Dinkydoe
(a) f is a density function if $\displaystyle \int_0^1f(x)dx = 1$

(b) $\displaystyle P(X>1/2) = \int_{\frac{1}{2}}^1f(x)dx$

(c) $\displaystyle \text{mean} = \int_0^1 xf(x)dx$
• Jun 30th 2010, 06:20 AM
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Quote:

Originally Posted by laurenng
I've never had a problem figuring out a problem before, and if I can't solve it I usually take the zero on that problem.

But this is a group work assignment and we have to each do a problem from a section that wasn't lectured on. If any one person doesn't have their section he won't accept any part from the group...

So of course I'm COMPLETELY lost.

In case it helps, I'm using "Calculus - Volume 2" by James Stewart. (It's one Calc book split into three smaller ones used at the University of Florida.) It's published by Thomson. The problem I have to do is section 8.5, number 6.

Let f(x)=kx^2 if 0<x<1 (these symbols should also have 'or equal to') and f(x)=0 if x<0 or x>1
a) For what value of k is f a probability density function?
b) For that value of k, find P(X>1/2) ('or equal to').
c) Find the mean.

Let me know if there's any other information you need to help me out. Thanks!

In order to have a probability density function, the area under the curve must equal 1. Does this give you some ideas?

Edit: Posted at about the same time as Dinkydoe, mine came out last..