There are 9 children in a class who take the bus to school, and there are 15 total children in the class. What percentage of the
2 answers:
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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
Option (A) represents the function and its inverse of a function option (A) is correct.
<h3>What is a function?</h3>
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function and inverse of a function shown in the picture.
Checking for option (A):
Taking f(x):
To find the inverse of a function interchange the x and y variables:
f(x) → x
x → g(x)
Solving:
4x = g(x) + 10
g(x) = 4x - 10
Similarly, we can find the inverse of a function.
Thus, option (A) represents the function and its inverse of a function option (A) is correct.
Learn more about the function here:
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