Step-by-step explanation:
There are 12 games in the population. You need to use a random number generator to choose 2 of these games.
RandomSample[{1,2,3,4,5,6,7,8,9,10,11,12},2]
Let's say the first sample you get is {1,5}. That corresponds to game times of 8 minutes and 7 minutes. The mean game time for that sample is 7.5 minutes. So the first row in your table would be:
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:
And if we take common factor we got:
And as we can see then we can conclude that