Mixed continuous / discrete probability question

[s195404]

Dear forum,

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.

:-)

[BGM]

Let be the mortality risk and be the number of deaths among the next 4 patients. I suppose the question mean



So the conditional probability is just to simple expression of a Binomial pmf, in terms of a variable in between 0, 1.

For the marginal probability, you will need to use the law of total probability



to compute the answer.