State the slope and y-intercept of the graph of 9

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

Christine owns 9 hair bands and additional hair bands are 2 for a dollar. How much money does she need to spend on hair bands in

kirill [66]

Answer: $20

Step-by-step explanation:

If she already has 9, and she needs 49, take that extra 9 off 49 and then she needs 40 more and she gets 2 for a dollar, she'll need to spend $20 to get 40 headbands. Can I please get Brainliest?

7 0

3 years ago

Find the measure of BCD

Lerok [7]

please mark me as brainliest!!

4 0

2 years ago

Complete the table of values for y=2xsquared+x

hodyreva [135]

The solution of y= $2x^{2} +x$ given as:

x: 0 1 2 3

y: 0 3 10 21

<h3>What is Linear Equation?</h3>

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Given function is:

y= $2x^{2} +x$

For finding the solution of above expression, take value of x and solve for y.

If x=0

y= 2(0)+0

y=0

If x=1,

y= $2(1)^{2} +1= 3$

If x=2

y= $2(2)^{2} +2=10$

If x=3

y= $2(3)^{2} +3=21$

The required table is:

x: 0 1 2 3

y: 0 3 10 21

Learn more about linear equation here:

brainly.com/question/488051

#SPJ1

8 0

2 years ago

Irene tutors fellow students to earn spending money. A designer purse she wants to buy is $170. She has already earned and set a

zimovet [89]

Answer:

A

Step-by-step explanation:

$170 - $51 = $119 more needed for the purse

she earns $17 per hour so

$119 ÷ $17 = 7

she should tutor 7 hours so h>10

4 0

3 years ago

State the slope and y-intercept of the graph of 9 – x = 2y