1 The continuous random variable X has p.d.f. f(x) where f(x) = ¿x for 0

A relatively rare disease D occurs with P(D)=0.01. There exists a diagnostic test such that: P(positive test | D)= 0.99 P(positive test | not D)=0.1 Using the bayes rule, what is P(D | positive test)?

Let X be a random variable corresponding to 2021 oil production in New Mexico relative to 2020.  Let Y be a random variable corresponding to 2021 oil production in Texas relative to 2020.   Suppose the joint distribution of X and Y is    f (x,y) = 4xy   for x,y SET [0,1] Find P (X < 1/2 | Y > 3/4)          ** X is less than or equal to 1/2  and Y is greater than or equal to 3/4