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Answer:
The daily shop productivity is 480 frames
Step-by-step explanation:
The daily machine productivity refers to the TOTAL production made in a day.
The problem says that a shop produces metal on two different machines. It means that you must take into account the daily production of each one for finding the total production.
The first machine produces 300 frames in a day.
The second machine produces 180 frames in a day too.
So, if the first and the second machines are working together in a single day, the TOTAL daily production is the sum of the production of each one.
Thus, the daily shop productivity is 480 frames
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