Arthur baked 1 7/12 dozen muffins. Nina baked 1 1/12 dozen muffins. How many dozen muffins did they bake?
2 answers:
Answer:
Total number of dozen muffins they both bake is
Step-by-step explanation:
Given : Arthur baked dozen muffins. Nina baked
dozen muffins.
We have to find the total number of dozen muffins did they both bake.
To find the total number of dozen muffins did they both bake is equal to number of dozen of muffins Arthur bake and number of dozen of muffins Nina bake
That is
Mathematically written as ,
Total number of dozen muffins = number of dozen of muffins Arthur bake + number of dozen of muffins Nina bake
Given : Arthur baked dozen muffins
and Nina baked dozen muffins.
Total number of dozen muffins =
Simplify, we get,
Total number of dozen muffins =
Adding, we get,
Total number of dozen muffins =
Thus, Total number of dozen muffins they both bake is
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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:
And if we take common factor we got:
And as we can see then we can conclude that