You multiply by -5 to find any next term. so next two are 500 then -2500
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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
P of selecting point on the shaded region = shaded area/whole area
<span>P( selecting point on the shaded ) = ( the four shaded circles ) / the whole square </span>
<span>P of selecting point on the shaded = ( 4 * ( π * r^2 ) )/ x^2 </span>
<span>P of selecting point on the shaded = ( 4 * ( π * (x/4)^2 ) )/ x^2 </span>
<span>P of selecting point on the shaded = ( 4 * ( π * x^2/16 ) )/ x^2 </span>
<span>P of selecting point on the shaded = ( π * x^2/4 )/ x^2 </span>
<span>P of selecting point on the shaded = x^2( π/4 )/ x^2 </span>
<span>P( selecting point on the shaded ) = π/4 ≈ 0.7854 ≈ 79%
=80%
D is right option hope this helps</span>
Answer: Its c 8-10
Step-by-step explanation:
