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!