Factor completely 4x^2-1
1 answer:
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Answer:
95
Step-by-step explanation:
let x be his mark in the fourth test, then
mean = = 83 ( multiply both sides by 4 )
83 + 81 + 73 + x = 332
237 + x = 332 ( subtract 237 from both sides )
x = 95
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