Show that for every $p$, $0\leq p\leq 1$, the function $f(x)$ = $p*sin(x) +(1-p)*cos(x)$, $0\leq x \leq \pi/2 $, and $f(x)=0$ otherwise, is a density function. Find its CDF and use it to find all the medians.
I was able to prove it a density function and also was able to get the CDF which is $(p +\sin(x) -p(\sin(x) + \cos(x))$ ; $0\leq x \leq \pi/2$ and $1$ for $ x\geq \pi/2$ and $zero$ elsewhere. (I hope I am correct)
I don't understand the last part. What do they mean by finding all the medians?