Probability Density Function

[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!

 

[tkhunny]

I thought by your description of how to find 'k' that you were headed the right direction. However but your fear against c1 and c2, perhaps not.

Hint: It is the same thing!

1) Find k by the method you described.

2) Evaluate the integral and solve: \(\displaystyle \int_{0}^{c_{1}}kx^2\;dx = 0.10\)

3) If you get c1 > 2, something went wrong.

 

[alakaboom1]

That's it. Thanks a lot!