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 
soh cah toa
that is the saying I use
we will use cah
c is cos
a is ajacent
h is hypotinuse
to find cos K we need to do
adjacent / hypotenuse
can you do that and write it in the comments
Number of cone left is 75 cone
<u>Given that;</u>
Cost of each cone = $3.75 each
Starting number of cone = 300
Total amount earn = $843.75
<u>Find:</u>
Number of cone left
<u>Computation:</u>
Number of cone sale = Total amount earn / Cost of each cone
Number of cone sale = 843.75 / 3.75
Number of cone sale = 225 cone
Number of cone left = Starting number of cone - Number of cone sale
Number of cone left = 300 - 225
Number of cone left = 75 cone
Learn more:
brainly.com/question/4115571?referrer=searchResults
Least to greatest: 0.7 0.9 0.73 0.81
Answer:D 2 1/7
Step-by-step explanation: you can put 7 into 15 two times and that gives you 2 holes and you then have 1/7 leftover therefore you have 2 1/7.