Answer:
This is an example of causation because the patient that took the medication recovered quicker than the patient that did not.
Step-by-step explanation:
Correlation is a statistical technique that shows that a relation exists between 2 variables but does not give any explanation about the relationship
Example: Correlation between Air Conditioner sales and sunglasses sold.
As the sales of the air conditioner is increasing so do the sales of sunglasses.
Causation is a statistical technique that shows a relation ship between 2 variable. It emphasizes the fact that any change in the value of one variable will cause a change in the value of another variable.
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:
.....................
Step-by-step explanation:
Answer:
92.75 cm^2
Step-by-step explanation:
Area of triangle ADC
= (1/2)×4.5×12 = 27
Area of triangle ACB
=(1/2)×12×5 = 30
Find AB using pythagoras theorem on triangle ABC:
AB^2 = 5^2 + 12^2 = 25 + 144
AB^2 = 169
AB = 13cm
Area of triangle AGB
= (1/2)×13×5.5 = 35.75
Total area = sum of the areas of the 3 triangles found above
= 27 + 30 + 35.75 = 92.75 cm^2
