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Oxana [17]
3 years ago
9

For each given p, let ???? have a binomial distribution with parameters p and ????. Suppose that ???? is itself binomially distr

ibuted with parameters ???? and ????. Formulate ???? as a random sum and show that ???? has a binomial distribution with parameters p???? and ????.
Mathematics
1 answer:
pshichka [43]3 years ago
8 0

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)

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One of the tables shows a proportional relationship.
beks73 [17]

Answer:

See attached

Step-by-step explanation:

The graph of a <u>proportional linear relationship</u> is a line that <u>passes through the origin</u> (0, 0).

From inspection of the given tables, the <u>linear equations</u> for each table of points is:

  • Table 1:  y = x + 1
  • Table 2:  y = x/2
  • Table 3:  y = x + 2
  • Table 4:  y = 2x + 1

The only equation for which y = 0 when x = 0 is y = x/2  →  Table 2.

Given points from Table 2:

  • (2, 1)
  • (4, 2)
  • (6, 3)
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To <u>graph the line</u>, plot the given points and draw a line through them (see attached).

5 0
2 years ago
How do you do 39 divided by 936 long division
viva [34]

936 <span>39 </span>= 24

24 = 240 to the nearest tenth

24 = 24 to the nearest hundredth

24 = 24 to the nearest thousandth

= 0 to the nearest tenth

= 0 to the nearest hundredth

= 0 to the nearest thousandth


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2 years ago
Which equation is correct regarding the measure of
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ep explanation:

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2 years ago
A bicycle wheel with radius 30cm made 1000 revolutions. What distance did it cover?​
Inga [223]

The distance covered by bicycle is 1.885 km.

What is distnace?

Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in ordinary language.

Given:  A bicycle wheel with radius 30cm made 1000 revolutions.

We have to find the total distance covered by bicycle.

First to find the circumference of the bicycle wheel.

Circumference = 2πr

where, r is the radius.

Here r = 30.

So,

Circumference = 2 x π x 30 = 60π

Now to find the total distance,

D = circumference x number of revolutions.

D = 60π x 1000

D = 188,495.5592 cm

D = 188,495.5592 /1000 km

D = 1.88 km

Therefore, the distance covered by bicycle is, 1.885 km.

To know more about the distance, click on the link

brainly.com/question/26046491

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8 0
1 year ago
Connor wants to drive from Tucson to the Grand Canyon a distance of 338 miles if he drives a steady rate of 52 mph how many hour
alexandr1967 [171]

Answer:

6.5 Hours

Step-by-step explanation:

Divide 338 by 52 to get the answer

5 0
3 years ago
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