Problem 7.1 (10 points) Let pXnqn"0,1,... be a Markov chain with state space S " t1, 2, 3u and transition probability matrix P " ¨ ˝ 0.5 0.4 0.1 0.3 0.4 0.3 0.2 0.3 0.5 ˛ ‚. (a) Compute the stationary distribution π. (b) Is the stationary distribution π also the limiting distribution? Give a reason for your answer.

Answers

Answer 1

Answer:

The responses to the given can be defined as follows:

Step-by-step explanation:

For point a:

fixing probability vector that is [tex]W = [a b c][/tex]

[tex]\therefore[/tex]

relation: [tex]WT =W[/tex]

[tex]\to 0.5a+0.3b+0.2c=a ..................(1)\\\\ \to 0.4a+0.4b+0.3c=b..............(2)\\\\ \to 0.1a+0.3b+0.5c=c.................(3)[/tex]

solving the value:

[tex]a=0.3387 \\\\ b=0.3710\\\\ c=0.2903[/tex]

Therefore the stationary distribution [tex]\pi =[0.3387 \ 0.3710\ 0.2903][/tex]

For point b:

[tex]\pi[/tex] will be limiting distribution if [tex]\pi_j=\lin_{n\to \infity} (X_n=\frac{j}{X_0}=i) \Sigma_{\sqrt{j}} n_j=1[/tex]

[tex]\pi[/tex] satisfies the above condition so, it is limiting the distribution.


Related Questions

What is the value of X?

Answers

Answer:

16

Step-by-step explanation:

AB = BC    

32[tex]\sqrt{2}[/tex] = [tex]\sqrt{2 *AB^{2} } \\ => AB = 32 = BC\\x= BC/2 => x = 32/ 2 = 16[/tex]

Solve the equation by completing the square. Round to the nearest hundredth if necessary.

x2 + 2x = 8

Answers

Answer

2

Step-by-step explanation:

(reorder terms)

2x + 2x = 8

collect like terms

4x=8

divide both sides of the equation

x = 2

A Stats test has 5 multiple choice questions with four choices with one correct answer each. If we just randomly guess on each of the 5 questions, what is the probability that you get exactly 2 questions correct

Answers

Answer:

0.0512

Step-by-step explanation:

Probability of making a correct guess ; p = 1 / 5 = 0.2

q = 1 - p = 1 - 0.2 = 0.8

Number of questions, n = 5

Using the binomial probability relation :

P(x = x) = nCx * p^x * q^(n-x)

P(x = 3) = 5C3 * 0.2^3 * 0.8^2

P(x = 3) = 0.0512

If angles A and Bare alternate interior angles, what is the measure of angle B
if angle A measures 105°?
O A. 90°
B. 75°
C. 180°
D. 105

Answers

D. 105

Alternate interior angles are congruent so angle A is congruent to angle B

Help!! No links!! step by step

Answers

if you download slader and choose the math book you are using it shows the answers for big ideas math:)

Help me this is giving my head a brain poop

Answers

Answer:

I suck at algebra. your on your own for this one buddy

Answer:

40 minutes

Step-by-step explanation:

I don't think the number of players affect the amount it takes to play the piece. The answer is probably still 40 minutes

Solve for 43.
43 = [?]
58°
139° 41°
43

Answers

Answer:

∠3 = 81

Step-by-step explanation:

Interior angles in a triangle add up to equal 180°

Hence, 58° + 41° + ∠3 = 180

58 + 41 = 99

99 + ∠3 = 180

* subtract 99 from each side *

99 - 99 cancels out

180 - 99 = 81

we're left with ∠3 = 81°

Find the area of a triangle with the following measures:

B-12 inches

H-5 inches

Answers

The area would 30 in^2
Reason:
Area of a triangle =1/2 bh
Area= 1/2 (12)(5)
Area =(6)(5) (because a half times 12 =6)
Therefore Area =30 in^2
Hopefully that helps, if not I apologize

help ASAP PLEASE look at it help plsease​

Answers

C because it’s in the middle of 60 and 62 , closer to the 62(:
it’s C

explanation-because if you count the amount of dashes between 60 and 62 you will find 9 dashes which means the middle dash is 61 so the dashes i between 60 and 61 and then 61 to 62 are counting by 2s.

Hope this helps!!

Gunther's starting weight is 248 pounds, and he plans to lose 2 pounds each week. Use a linear equation to determine Gunther's weight after 10 weeks. What linear equation??

NEED HELP ASAP DUE TODAY!!! PLEASE AND THANK YOU :)

Answers

Answer:

......

Step-by-step explanation:

With these types of problems, it's best to label the unknowns and figure out an equation for what we want to find. Here, we're interested in weight in pounds, which I'll call W, as a function of the number of weeks that have gone by, which I'll call n. So if we can get an equation that relates W to n, we can answer the question of "how many weeks to reach 175 pounds?" by plugging in W = 175 to our equation and solving to find out what value of n gives us that.

Suppose Alex weighs P pounds at the start of his diet. We don't know what P is yet, but we'll aim to find its value later with the information the question gives us.

After 1 week, Alex will lose 2 pounds and will weigh P - 2 pounds

After 2 weeks, Alex will lose another 2 pounds and weigh (P - 2) - 2 = P - 4 pounds

After 3 weeks, Alex will weigh (P - 4) - 2 = P - 6 pounds

You can see the pattern here: after every week, knock off 2 pounds. So in general after n weeks, Alex will lose 2n pounds from his start weight, and he will weigh P - 2n

That gives the equation W = P - 2n, or equivalently

W = -2n + P

We can recognize this as a linear equation, which takes the form y = mx + b, where:

- x is the independent variable,

- y is the dependent variable (the thing that changes as a function of x),

- m is the slope (how much y changes for every unit change in x), and

- b is the y-intercept (that is, the value of y when x = 0).

In our equation W = -2n + P, the number of weeks n is the independent variable, weight W is the dependent variable (it varies as a function of the number of weeks), -2 is the slope (because Alex weight 2 pounds less for every week that goes by), and P - whose value we don't know yet - is Alex's starting weight (i.e., the value of W when n = 0).

To find the value of P, we can use the information in the question that after 6 weeks, Alex weighs 205 pounds. In other words, when n = 6, W = 205. Plug that into our equation and get:

205 = P - 2*6

We can solve that for P:

205 = P - 12

Add 12 to both sides:

P = 205 + 12 = 227

So Alex weighs 227 pounds when he starts the diet, and we have

W = -2n + 227

This is the linear equation the question is asking for.

To find how many weeks Alex needs to reach his target weight of 175 pounds, set W = 175 in the equation and solve it for n:

175 = -2n + 227

Move the -2n over to the other side:

2n + 175 = 227

Subtract 175 from both sides:

2n = 227 - 175

2n = 52

Divide both sides by 2:

2n/2 = 52/2

n = 26

So if he keeps losing 2 pounds per week, Alex will reach his target weight of 175 pounds after 26 weeks.

Of course in real life weight loss doesn't necessarily work like in this question (usually, the rate of loss slows down closer to the goal and the body adapts to eating less). But for the purposes of this question and with this simple linear model of weight loss, Alex would reach his goal weight in half a year.

(a+b)⁴ binomial expansion

Answers

Answer:

[tex]\huge\boxed{Answer\hookleftarrow}[/tex]

Method Used :-

[tex]Using  \: (a+b) {}^{2} (a+b) {}^{2} and (a+b+c) {}^{2} [/tex]

Expansion :-

[tex](a + b) {}^{4} \\ = [(a+b) {}^{2} ] {}^{2} \\ = (a {}^{2} +2ab+b {}^{2} ) {}^{2} \\ = (a {}^{2} ) {}^{2} +(2ab) {}^{2} +(b {}^{2} ) {}^{2} +2(a {}^{2} )(2ab) +2(2ab) \\ (b {}^{2} )+2(b {}^{2} )(a {}^{2} ) \\ = a {}^{4} +b {}^{4} +4a {}^{3} b+6a {}^{2} b {}^{2} +4ab {}^{3} [/tex]

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

# ꧁❣ RainbowSalt2²2² ࿐

The radius of a circle is 12 yards. What is the circle's area?

Answers

The area of the circle is 452.4

Simplify 7(A-6) need help

Answers

Answer:

7a - 42

Step-by-step explanation:

1st step is to distribute.

7(a-6)

multiply 7 to "a" and -6

7a - 42

Please help me out this is not very easy for me.

Answers

Answer:

A

Step-by-step explanation:

find the missing side of the triangle​

Answers

Answer:

12

Step-by-step explanation:

Use pythag to solve.

x^2+5^2=13^2

x=12

Can someone please tell me if this angle is supplementary or complementary

Answers

Answer:

Step-by-step explanation:

Since the angles both come off of the straight line, they are supplementary, and they add up to equal 180 degrees.

2x + 4x + 24 = 180 and

6x + 24 = 180 and

6x = 156 so

x = 26

Help answer correctly !!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!

Answers

Answer:

dunno

Step-by-step explanation:

It might be 1,400?

Hope it works!!

What is the equation
in slope-intercept
form of the line that
passes through the
points (20,-25) and
(-8, -11)?

Answers

Answer:

y = -1/2x - 15

Step-by-step explanation:

y2 - y1 / x2 - x1

-11 - (-25) / -8 - 20

14 / -28

= -1/2

y = -1/2x + b

-11 = -1/2(-8) + b

-11 = 4 + b

-15 = b

I need help quick, please

Answers

Answer:

B

Step-by-step explanation:

The shape is maintained exactly, it is rotated, not reflected and we can see it became smaller, so dilate it by a value less than one, but greater than 0. (2/3)

Given f(x) = x^2 + 2 and g(x) = 2 – x, find a simplified expression for f(2x) + g(3x).

Answers

Answer:

f(2)+g(3) = 5

Step-by-step explanation:

Given that,

f(x) = x² + 2

g(x) = 2-x

We need to find the value of f(2)+g(3).

f(2) = 2² + 2 = 6

g(3) = 2 – 3 = -1

So,

f(2)+g(3) = 6+(-1)

= 5

Hence, the value of the given expression is 5.

Which pattern or sequence did she use?

Answers

Answer:

b

Step-by-step explanation:

Find missing measure

Answers

Answer:

60°

Step-by-step explanation:

360 - ( 80+115+10) = 60°

The proof that point (1,3) lies on the circle that is centered at the origin and
contains the point (0, 2) is found in the table below. What is the justification
for the 5th statement?
Statement
Justification
A circle is centered at (0, 0) and
contains the point (0, 2).
Given
Definition of radius
The radius of the circle is the distance
from (0, 0) to (0, 2).
The distance from (0, 0) to (0, 2) is
VO-D) +(2-0) - 127-2
Distance formula
Definition of a circle
If (1, 3) lies on the circle it must be
the same distance from the center as
(0, 2).
The distance from (1, 3) is
VO - 1)2 - (0-3)? - v1+3 - 2
Since (1, 3) is 2 units from (0, 0), it
lies on a circle that is centered at the
Definition of a circle

Answers

The justification for the 5th statement regarding the circle is the distance formula.

How to depict the formula?

It should be noted that the distance between the points will be found based on the information given.

From the information given, the distance from (0, 0 to (0, 2) will be:

= [tex]\sqrt{0 - 0}[/tex]² + [tex]\sqrt{2 -0}[/tex]²

= 4

= 2

In this case, the justification is the distance formula.

Learn more about circle on:

brainly.com/question/12529233

#SPJ1

)If there are 6 builders, it takes 80 days to complete the house. How many builders must be employed to build the house in just 16 days?​

Answers

Answer:

64 builders must be employed to build a house in 16 days

what is 500+222+221 and

Answers

Answer:

943

Hope that this helps!


A rectangular prism has a length of 5 cm, a width of 2. 25 cm, and a height of 0.5 cm.
What is the surface area of the rectangular prism?
A. 5.625 cm2
B. 7.25 cm2
O C. 14.875 cm
D. 29.75 cm?

Answers

D. 29.75 is Right answer...

I hope you understand....

PLEASE HELP 50 POINTS
Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis, each salesman earns his paycheck differently. Salesman A works strictly on commission. He earns $65 per sale, with a maximum weekly commission of $1,300. Salesman B earns a weekly base salary of $300, plus a commission of $40 per sale. There are no limits on the amount of commission he can earn. Salesman C does not earn any commission. His weekly salary is $900.

Verbally describe what each ordered pair in the first row of your table (when s = 0) means in terms of the situation. Use complete sentences in your answer.

Answers

Answer:

12 sales

Let x represent the number of sales each man had.

For Salesman A, he earns $65 per sale; this is 65x.

For Salesman B, he earns $40 per sale; this is 40x.  We also add to this his weekly salary of $300; this gives us 40x+300.

Since their pay was equal, set the two expressions equal:

65x = 40x+300

Subtract 40x from each side:

65x-40x = 40x+300-40x

25x = 300

Divide both sides by 25:

25x/25 = 300/25

x = 12

Step-by-step explanation:

plz brainlist

Answer:

The other person is correct

Step-by-step explanation:

please help I don't know what to do ​

Answers

Answer:

Slope of a line parallel is -5/9.

Slope of a line perpendicular is 9/5.

Step-by-step explanation:

5x + 9y = 1

To find the slope of this line we convert the equation to slope-intercept form ( y = mx + c where m is the slope).

9y = -5x + 1

y = -5/9 x + 1/9

So its slope (m)  is -5/9.

So slope of a line parallel to this is also -5/9.

Slope of a line perpendicular = -1 / -5/9

= 9/5.

Evaluate the algebraic expression 4y + x - w, when w = 12, x = 10, y = 5 and z = 9.
A. 7
B. 8
C. 18
D. 42

Answers

Answer:

The answer is C. 18

Step-by-step explanation:

4(5)+10-12=18

Hope this helps!

Five friends each conducted different studies comparing two variables. Each friend calculated the correlation coefficient, r, for their variables. Which r values suggest strong linear relationships? Select all that apply.

Answers

Answer:

The strong linear relationships are:

r = 0.95

r=-0.83

Step-by-step explanation:

When we have points whit apparent linear tents, we can fit the curve to a line and when the correlation coefficient (r) is equal to 1, we have perfect correlation and when r is equal to 0 we do not have a correlation.

Therefore r =  0.95 suggest strong linear relationships.

Now, we can use the same analysis with a negative value of r, so r = -0.83 is strong too.

I hope it helps you!

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