Answer:
See the proof below.
Step-by-step explanation:
Assuming this complete question: "For each given p, let Z have a binomial distribution with parameters p and N. Suppose that N is itself binomially distributed with parameters q and M. Formulate Z as a random sum and show that Z has a binomial distribution with parameters pq and M."
Solution to the problem
For this case we can assume that we have N independent variables 
with the following distribution:
bernoulli on this case with probability of success p, and all the N variables are independent distributed. We can define the random variable Z like this:
From the info given we know that 
We need to proof that 
by the definition of binomial random variable then we need to show that:
The deduction is based on the definition of independent random variables, we can do this:
And for the variance of Z we can do this:
![Var(Z)_ = E(N) Var(X) + Var (N) [E(X)]^2](https://tex.z-dn.net/?f=%20Var%28Z%29_%20%3D%20E%28N%29%20Var%28X%29%20%2B%20Var%20%28N%29%20%5BE%28X%29%5D%5E2%20)
![Var(Z) =Mpq [p(1-p)] + Mq(1-q) p^2](https://tex.z-dn.net/?f=%20Var%28Z%29%20%3DMpq%20%5Bp%281-p%29%5D%20%2B%20Mq%281-q%29%20p%5E2)
And if we take common factor 
we got:
![Var(Z) =Mpq [(1-p) + (1-q)p]= Mpq[1-p +p-pq]= Mpq[1-pq]](https://tex.z-dn.net/?f=%20Var%28Z%29%20%3DMpq%20%5B%281-p%29%20%2B%20%281-q%29p%5D%3D%20Mpq%5B1-p%20%2Bp-pq%5D%3D%20Mpq%5B1-pq%5D)
And as we can see then we can conclude that
Answer:
$997
Step-by-step explanation:
Okay, so the first thing you need to do is find how much commission Luis received so that we can add that to the base salary. To do that, we could set up a proportion.
Since percentages are out of 100, we'll need to put 14 over 100. Because $6050 is the total amount he sold, we'll put that number in the denominator corresponding to the total, or 100. The proportion will look somewhat like the following:
To find X, we have to multiply across (14 × 6050, which is 84700) then divide that by 100 (or the denominator right on the other side), which would result in 847.
So... X = $847. Now we add that to the base salary (150 + 847), and that gets us $997 for the total he was paid last week.
I apologize for taking so long to help ^-^;
Let's called the number we're searching for x.
We have 1/3=x/16. Multiply by 16 on both sides : x=16/3
