Hello I am trying to figure out a few parts of the following question:
We consider a random selection of coins where the probability of heads, C for the coins is a random variable whose pdf is $ f_c = k*c $ for $ 0 \leq c \leq 1 $.
a) Find k.
For this part I integrate $f_c$ from $ \infty $ to $ -\infty$ and set it equal to 1 and solve for k. I get 2.
b). Find P(H) for a single coin toss.
I am having trouble understanding what this part means. My understanding is that the $ f_c $ is distribution of different possible probabilities for a head. I don't see how to generalize this to a get a single probability.
