Please help me out thank you.
1 answer:
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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
Answer:
x = - 1
Step-by-step explanation:
The equation of the axis of symmetry for a parabola in standard form
y = ax² + bx + c : a ≠ 0 is found using
x = -
y = - x² - 2x - 5 ← is in standard form
with a = - 1 and b = - 2, thus equation of axis of symmetry is
x = - = - 1
Equation of axis of symmetry is x = - 1