What is the situation from the problem
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
Question:
A sample of cans of peaches was taken from a warehouse, and the content of each can mearsed for weight. the sample means was 486g with stand deviation 6g. state the weight percentage of cans with weight:
Draw normal curve to help - split into 8 section ( i can't draw it here)
a) 34.13% of cans will be between 480g and 486g.
b) 13.59 + 2.15 + 0.13= 15.87% of cans greater than 492g.
Look at the Stand Dev Graph where the give you the number
Step-by-step explanation:
Let me give you a different question and i will answer it, which you help you answer your question.
You write the problem as a mathematical expression
3x^2 + 30x + 75 =
Factor: 3 out of 3x^2 + 30x + 75.
3 (x2 + 10x + 25)
Factor using the perfect square rule.
And then your answer should be 3 ( x + 5) ^2
Step-by-step explanation:
here's your answer hope it helps you
