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borishaifa [10]
3 years ago
7

X^2-11x+30=2 Solve using quadratic formula or factoring

Mathematics
1 answer:
Pavel [41]3 years ago
7 0
X^2-11x+28=0

(x-7)(x-4)=0

x-7=0
x=7

x-4=0
x=4
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Find the slope of every line that is parallel to the graph of the equation. Y= 1/2x+4
Ostrovityanka [42]
For a line to be parallel it has to have the same slope as the original line. so the slope is 1/2 
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3 years ago
For each given p, let ???? have a binomial distribution with parameters p and ????. Suppose that ???? is itself binomially distr
pshichka [43]

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 X_i with the following distribution:

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Z = \sum_{i=1}^N X_i

From the info given we know that N \sim Bin (M,q)

We need to proof that Z \sim Bin (M, pq) by the definition of binomial random variable then we need to show that:

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The deduction is based on the definition of independent random variables, we can do this:

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And for the variance of Z we can do this:

Var(Z)_ = E(N) Var(X) + Var (N) [E(X)]^2

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And if we take common factor Mpq we got:

Var(Z) =Mpq [(1-p) + (1-q)p]= Mpq[1-p +p-pq]= Mpq[1-pq]

And as we can see then we can conclude that   Z \sim Bin (M, pq)

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