I am having a dreadful time making progress with the following problem, and would greatly appreciate any pointers you had.
The problem gives a mortality risk as the function f(x) = 20(1-x)/9 for 0.1 < x < 1, and 20x for 0 < x < 0.1. We need to find both the conditional and the marginal probabilities of exactly 3 deaths among the next 4 patients, assuming the number of deaths follows a binomial distribution.
With other problems, we are given f as a function of both x and y, and it is straightforward to find the conditional pdf as
h(y|x) = f(x,y) / f1(x)
and the marginal distribution as
f1(x) = int from -inf to inf f(x,y) dy.
I assume I need to do something along these lines, but getting to f(x,y) from my specific information is giving me a headache. I would be very grateful to anyone who could get me started with this, please. Thank you in advance.