Explanation:
Lets interpret Z with M trials. First we have M trials, each trial can be a success or not. The number of success is called N. Each trial that is a success becomes a trial, and if it is a success it becomes a success for Z. Thus, in order for a trial to be successful, it needs first to be successful for the random variable N (and it is with probability q), and given that, it should be a success among the N trials of the original definition of Z (with probability p).
This gives us that each trial has probability pq of being successful. Note that this probability is pq independently of the results of the other trials, because the results of the trials of both N and the original definition of Z are independent. This shows us that Z is the total amount of success within M independent trials of an experiment with pq probability of success in each one. Therefore, Z has Binomial distribution with parameters pq and M.
Answer: the option A.
The elimination method consist is adding the two equations in a way that one variable be eliminated..
In order to do that you might have to manipulate on of the equations prior to add the two equations.
In this case, ff you multiply the second equation by - 1 you will get
- x - y = - 4
which you can add to the first equation
2x + y = 8 to eliminate the y.
