# Math Help - Probability Density Function

1. ## Probability Density Function

I'm sorta confused by this question on a probability density function:

Let f(x) = kx^2 if 0< x < 2 and 0 otherwise. Find k such that f(x) qualifies as a continuous probability density function for a random variable X. Then find c1 and c2 such that P(X< c1)= 0.1 and P(X< c2)= 0.9

I guess we need to start by solving for k. To do that, we need to set the integral of f(x) from 0 to 2 equal to 1, right? Please correct me if I'm wrong. Anyways, what I'm really confused about is the second part. I just cant figure out how to go about finding 2 random values...

Thanks in advance if anyone can help!

2. Originally Posted by alakaboom1
Let f(x) = kx^2 if 0< x < 2 and 0 otherwise. Find k such that f(x) qualifies as a continuous probability density function for a random variable X. Then find c1 and c2 such that P(X< c1)= 0.1 and P(X< c2)= 0.9
Find $\mathbf k$ such that $k\int\limits_0^2 {x^2 dx} = 1.$

3. Thank you, but I said I already had that . I mainly need help with the second part of the problem.

4. Originally Posted by alakaboom1
I'm sorta confused by this question on a probability density function:

Let f(x) = kx^2 if 0< x < 2 and 0 otherwise. Find k such that f(x) qualifies as a continuous probability density function for a random variable X. Then find c1 and c2 such that P(X< c1)= 0.1 and P(X< c2)= 0.9

I guess we need to start by solving for k. To do that, we need to set the integral of f(x) from 0 to 2 equal to 1, right? Please correct me if I'm wrong. Anyways, what I'm really confused about is the second part. I just cant figure out how to go about finding 2 random values...

Thanks in advance if anyone can help!
Solve $\displaystyle \int_{0}^{c_1} f(x) \, dx = 0.1$ for $c_1$. Other one done in same way.

5. Ah, thats it. Thanks a lot!