I'm having quite a large issue recognizing which distribution to use in a given task.
I know the mathematical definitions for each of them, but I'm unable to apply them in real problems. Is there like an easy way or recognizing which one to use to solve the problem?
Like for e.g.
For poisson distribution, the "event" usually happens on a given timeframe( like daily, weeklly etc. ) or we're given some kind of an average value.
For hypergeometric distribution, usually we need to pick k objects of a set with n objects with some kind of a special property.
The ones I'm having trouble with are binomal, negative binomal and geometric.
Let's see the following problem:
We have a lab. consisting of 20 computers. 5 students need to take an exam. The probability that the computers have the exam software installed is 1/3.
a) What's the probability that there will be enough computers for the students in a single lab?
b) The professor turns the computers on one by one and checks if the software is installed. Describe the random variable "amount of turned on computers until a working one is found" (this is geometric distribution, number of failures before success happens)
c) The professor turns the computers on one by one, checks if the software is installed and puts a student on it if it's working. What's the probability that all the students will take the exam in the same lab? (this looks to me like negative binomal? Not sure.)
d) If the professor knows that the software is installed on 7 computers, what's the probability that he will find those 7 computers if he picks the first half of the turned on computers? (hypergeometric? 10 computers picked, 7 have special property?)
Tl;dr What's the easiest way to recognize which random variable distribution needs to be used in a task?