Insert one set of parentheses in each numerical expression so that it equals the stated amount.

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:

$X_i Bin (1,p) = Be(p)$ 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:

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

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:

$E(Z) = Mpq$

$Var (Z) = Mpq(1-pq)$

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

$E(Z) = E(N) E(X) = Mq (p)= Mpq$

And for the variance of Z we can do this:

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

$Var(Z) =Mpq [p(1-p)] + Mq(1-q) p^2$

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 $Z \sim Bin (M, pq)$

8 0

3 years ago

PLZZ HELP ITS AN EMERGENCY THIS IS DUE IN 30 MINUTES!!!

Nataly_w [17]

Answer:

1.equation

2. inverse operations

3. 3.7

4. 8

5. yes its a solution because 58=58

6. not a solution

7. 10.3

9. 9

11. 64

12. 2.1

Step-by-step explanation:

4 0

3 years ago

Which number line shows the estimate of square root of 47 in the correct interval of integers

mr_godi [17]

Answer:

B

Step-by-step explanation:

Because yes

8 0

3 years ago

Read 2 more answers

What is the interest on Rr 20,000 if the interest rate is 15%?

Basile [38]

Answer: Rr.3,000

Step-by-step explanation:

The interest is the amount that accrues on a principal that was invested or a cost that was incurred.

It is based on a certain interest rate which in this case is 15%.

The principal is Rr. 20,000.

Interest = Principal * Interest rate

= 20,000 * 15%

= Rr.3,000

3 0

3 years ago

Write two expressions to show the total area of advertisement space on one page.

valina [46]

The area covered by the advertisement on the page is $ab \ unit^2$ .

<h3>What is the definition of area of a rectangle?</h3>

The area of a rectangle covers is the space it takes up inside the boundaries of its four sides. The dimensions of a rectangle determine its area. In general, the area of a rectangle is equal to the product of its length and breadth of the rectangle.

The formula of area of rectangle is $length \times breadth$ $unit^2$