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:
The perimeter is 54 square units
Step-by-step explanation:
You find the sum of 12+12 and that's 24, and 15+15, and that is 30, and 30+24 is 54.
Hope this helped!
Answer:
-9/4, -0.75, -6/10, 5/3, 2.1
Step-by-step explanation:
This is a lot easier to figure out if you simplify the fractions and then change them to decimals
So -9/4 = -2 1/4 or -2.25
-0.75
-6/10 = -0.60
5/3 = 1 2/3 or 1.67
2.1
When you are ordering negatives, the biggest negative is the least. That is why -9/4 (-2.25) is the least number out of the five given.
The next one would be -0.75, because it is the second biggest negative fraction.
The next one is -0.60 because that is the 3rd biggest negative fraction (or the smallest because this is the last negative)
Now, because we're in the positives we start with 1.67, because it is smaller than the other number.
2.1 is our last number, so it is the greatest!
I hope this helped :)
Answer:20
Step-by-step explanation:
<h2>im pretty sure it is... 56,280?</h2>
