A system has three possible states, 0, 1 and 2. Every hour it makes a transition to a different state, which is determined by a coin flip. For example, from state 0, it makes a transition to state 1 or state 2 with probabilities 0.5 and 0.5.
a. Find the transition probability matrix.
b. Find the three-step transition probability matrix.
c. Find the steady-state distribution of the Markov chain.

Answers

Answer 1

Answer:

Step-by-step explanation:

From the given information;

the transition probability matrix (TPM) for state 0, 1, 2 is:

[tex]P =\left[\begin{array}{ccc}0&0.5&0.5\\0.5&0&0.5\\0.5&0.5&0\end{array}\right][/tex]

The three-step TPM  is done by a simple matrix multiplication which is computed as follows:

[tex]P^3 = \left[\begin{array}{ccc}0.250&0.3757 &0.375\\0.375&0.250&0.375\\0.375&0.375&0.250\end{array}\right][/tex]

The steady-state distribution of the Markov Chain is  determined by first solving the system πp = π together with the normalizing condition

here;

π₁ + π₂ + π₃ = 1

So;

0.5π₂ + 0.5π₃ = π₁

⇒ π₂ + π₃ = 2π₁

0.5π₁ + 0.5π₃ = π₂

⇒ π₁ + π₃ = 2π₂

0.5π₁ + 0.5π₂ = π₃

⇒ π₁ + π₂ = 2π₃

Thus, π₁ + π₂ + π₃ = 1

This can be re-written as:

1 - π₁ = 2π₁

1 - π₂ = 2π₂

1 - π₃ = 2π₃

1 = 3π₁

π₁ = 1/3

1 = 3π₂

π₂ = 1/3

1 = 3π₃

π₃ = 1/3

Hence, the steady-state probability distribution is π = [1/3, 1/3, 1/3]


Related Questions

Hi I need help please

Answers

Answer:

Trapezoid. Big to small = 3:1

Square. Enlargement

Step-by-step explanation:

base 1 of trapezoids respectively big to small are 6:2 or 3:2

The purple shape is an enlarged form of the black square.

If my answer is incorrect, pls correct me!

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-Chetan K

What would you estimate for the length of a bass clarinet, assuming that it is modeled as a closed tube and that the lowest note it can play is a Db whose frequency is 69.3 Hz

Answers

I just looked it up soo
Hope this helps :D

Please help! With math problem:))

Answers

Answer:

B - -1

Step-by-step explanation:

x+y=1

x-y=3

x-y +y = 3 +y

x=3 +y

x+y =1

(3+y) +y=1

3 + 2y= 1

2y= -2

y= -1

Answer B - - 1



Vdhdijddbbdgdhdjdjdbd hope that answer helps


Clark has two 16-ounce cans of corn. He uses 18 ounces of it to
make a corn soup and the rest to make a casserole.
a. How many ounces of corn did he use to make the casserole?

Answers

Answer:

14

Step-by-step explanation:

Answer:

14 Ounces

Step-by-step explanation:

16 x 2 = 32 Ounces of corn

32 - 18 = 14 Ounces

Roper works 40 hours per week regularly , at a rate of 16.20 per hour. When he works over time his rate is time and a half of his regularly hourly rate . What is his hourly overtime rate ?
A) 24.30
B)25.67
C)26.50
D)27.54

Answers

Answer:

over time pay would be $24.30/hr

16.20 +(1/2 16.20) = 24.30

given m||n, find the value of x. see attachment.

Answers

Answer:

6x-8=5x+14

x=22

this is the solution

(6x-8)°=(5x+14)°

_ _ _ _ _ +14= _ _ _ _ _ _-8= x=14+8=22°

(6×22-8)°=124°

(5×22+14)=124°

The area of the kite is 30 m2. What is the value of x? Explain

Answers

Answer:

The area of a kite measures the space inside the four sides. The most common way to find the area is by using the formula A = xy/2, where x and y are the lengths of the diagonals.

Step-by-step explanation:

Which of the following did not occur during the reign of Diocletian? A. Church leaders were arrested. B. Christians were crucified for burning Rome. C. Churches and Christian writings were burned. D. Christians were required to offer sacrifices. Please select the best answer from the choices provided A B C D

Answers

Answer: B is the answer

Step-by-step explanation:

Answer:

B (Christians were crucified for burning Rome)

Step-by-step explanation:

im sorry if this is wrong but i looked it up and it seemed to be the right answer im taking the 2021 edge exam rn

in the rectangle below, AE=2x+8, CE=5x+4, and m

Answers

Answer: 2x+8=12, 5x+4=29

Step-by-step explanation:

2x2=4+8=12

5x5=25+4=29

please help me. justify your answers!​

Answers

Answer:

g. True

h. False

i. False

Step-by-step explanation:

g.

[tex]\frac{1}{14}[/tex] is half of [tex]\frac{1}{7}[/tex]

This would be true because half of a number can be found by multiplying by [tex]\frac{1}{2}[/tex]

If you multiplied [tex]\frac{1}{7} * \frac{1}{2}[/tex]

The numerator is 1 * 1 which is 1

And then the denominator is 7 * 2 which is 14

That would give you [tex]\frac{1}{14}[/tex]

h.

The products of two reciprocals is 0

This is not true

Reason being, reciprocals are just the number flipped. If you times the number by itself, you don't get 0, you get 1.

Ex: [tex]\frac{2}{8}[/tex]

Its reciprocal is [tex]\frac{8}{2}[/tex]

So multiply them together

[tex]\frac{2}{8}* \frac{8}{2}[/tex]

2 * 8 = 16

8 * 2 = 16

[tex]\frac{16}{16} = 1[/tex]

i.

A whole number does not have a reciprocal

This is incorrect. If you think about it, a whole number is just the number, over 1

Ex: [tex]\frac{6}{1}[/tex]

This is still a whole number even though its written in fraction form because if you divide 6 by 1, your still going to get 6.

If you an write it as a fraction, it has a reciprocal.

The reciprocal in this case would be [tex]\frac{1}{6}[/tex]

I hope this helps, don't be afraid to reach out with any further questions!

Answer:

T, F, F

Step-by-step explanation:

The half-life a particular radioactive
substance is 1 year. If you started with
50 grams of this substance, how much
of it would remain after 3 years?
First, complete the equation:
Remaining Amount =

Answers

Answer:

Remaining amount is 6.25 gram

Step-by-step explanation:

After one year what you would be left with is 50/2 which is 25 gram

After the second year, you would be left with 50/4 which is 12.5

After the third year what's left is 50/8 i.e 6.25

Log(10) u = 3/2 log(10) 4

Answers

u = 8

Step-by-step explanation:

log(10) u = log(10) 4^(3/2)

or

u = 4^(3/2)

= [sqrt(4)]^3

= (2)^3

= 8

NO LINKS OR ELSE YOU'LL BE REPORTED! Only answer if you're very good at Math.

Find the slope of each line using the rise/run formula.​

Answers

Answer:

-3/1 and 7/3

Step-by-step explanation:

First one go down 3 and right 1.

Second one go up 7 and right 3.

HELP PLEASE I WILL GIVE EVERYTHING JUST HELP.

How do you do this

Answers

Answer:

156 or 468

Step-by-step explanation:

for 156

13*12

for 468

13*12*3

plz solve it CORRECTLY step by step plz​

Answers

Answer:

Step-by-step explanation:

area of circle=π[tex]r^{2}[/tex]

=22/7*[tex]21^{2}[/tex]

=22/7*441

=9702/7

=1386 [tex]cm^{2}[/tex]

Answer:

1386cm sq

Step-by-step explanation:

formula to find area of circle is 22/7*radius sq

which is 22/7 * 21 * 21

= 22 * 3 * 21

= 1386

Hope this is helpful. Please mark brainliest....

5
Select the correct answer from each drop-down menu.
d
60°
30°
D
The product of sin 30° and sin 60° is same as the product of
vand

Answers

Answer:

The product of sin 30° and sin 60° is the same as the the product of cos 30° and cos 60°.

The product of sin 30° and sin 60° is same as the product of cos 30° and cos60°.

What is Trigonometry?

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We know that the sine function is a ratio of opposite side and hypotenuse.

The cosine function is a ratio of Adjacent side and hypotenuse.

Let us find the product of sin 30° and sin 60°

=sin 30°.sin 60°

=1/2.√3/2

=√3/4

Now we know that  cos 60° is 1/2 and  cos 30° is √3/2

Product cos 60° and cos 30°

cos 30°.cos 60°=1/2.√3/2

=√3/4

Hence, the product of sin 30° and sin 60° is same as the product of cos 30° and cos60°.

To learn more on trigonometry click:

https://brainly.com/question/25122835

#SPJ7

how can you tell if a function is linear or nonlinear from a table​

Answers

You can tell if a table is linear by looking at how X and Y change. If, as X increases by 1, Y increases by a constant rate, then a table is linear. You can find the constant rate by finding the first difference . This table is linear.

I really need help plsssssssssssssss help

Answers

Answer:

first spot 10, second 16, third 18, fourth 22

Answer:

The expression that represents the table is

y=4+2x

when x=3

y=4+2(3) = 10

When x=6

y=4+2(6)= 16.

Do this for all the values of x and you'll get the corresponding value for y

10

16

18

22.

Your answer would be

A car cost $19,956 How much will it cost a company to buy nine cars for its salespeople?

Answers

Answer:

179,604

Step-by-step explanation:

MARK ME BRAINLIST

Answer:

It will cost the company $179,604.

Step-by-step explanation:

Multiply the cost of 1 car by the number of cars needed:

19,956 × 9

179,604

what is the value of x ?

please help me!!!

Answers

Answer:

The letter "x" is often used in algebra to mean a value that is not yet known. It is called a "variable" or sometimes an "unknown". In x + 2 = 7, x is a variable, but we can work out its value if we try! A variable doesn't have to be "x", it could be "y", "w" or any letter, name or symbol.

Step-by-step explanation:

Answer:

x=14

Step-by-step explanation:

4x+2x+6=90

6x=84

x=84/6=14

I need to find x based off of the models

Answers

Answer:

2. 9x - 4= 12x - 55

9x - 12x = -55+4

-3x = -51

x = 17

3. 7x +29 = 11x - 31

7x - 11x = -31-29

-4x = -60

x =15

I AM GIVING 50 POINTS :))



The volume of the prism is 81m3

What is the volume of a pyramid that has the same base and height as this prism?

____m3

Answers

Answer:

16 x 25 x 37 = 14800 m^3

////////////////////////

How many square feet of outdoor carpet will we need for this hole

Answers

The hole should need 38ft^2 of carpet

f(x) = - 2x - 3
g(x) = 3x + 1
Find (f .g)(x).

Answers

Answer:

-6x² - 11x - 3

Step-by-step explanation:

This represents the product of the two functions.

(-2x-3)(3x+1) = -(2x+3)(3x+1) = -(6x² + 11x + 3) = -6x² - 11x - 3

Find the quotient for 5,600÷8​

Answers

Answer:

700

Hope this helps!!

Answer:

700

Step-by-step explanation:

Please help me and show work please

Answers

Answer:

[tex]x=2[/tex]

Step-by-step explanation:

Since the scale is in equilibrium, both sides must be equal. Therefore, we have the following equation:

[tex][\text{Left Side} ]3x+3=[\text{Right Side}]9[/tex]

Solving for [tex]x[/tex]:

[tex]3x+3=9,\\3x=6,\\x=\boxed{2}[/tex]

Answer:x=2

Step-by-step explanation: try to first set up an equation. First we can see the scale is balanced so we know each side is equal to each other. You have 3 x boxes and 3 circles so our first side will be 3x+3. Now let’s move onto the second side. It has 9 circles so 3x+3=9. Now let’s solve!

Subtract 3

3x=6

Now divide by 3

X=2

Hope this helps

Select the graph of y = tan x

Answers

Answer:

Graph B

Step-by-step explanation:

Answer:

B) is correct

Step-by-step explanation:

Which of the following fractions is not equivalent to 2?

3/6 10/5 2/1 (1 4/4)

Answers

Answer:

3/6.

Step-by-step explanation:

3/6 is 0.5, not 5.

Answer:4/4

Step-by-step explanation:

Find the equation of a line from the table:
X) (y)
6 14
7 17
8 20
9 23
10 26

A. Y= 3x + 4
B. Y= 2x + 4
C. Y= 2x - 4
D. Y= 3x - 4

Answers

I don’t know but c i guess

Simplify the following expression 10s-8s+2s=

Answers

Answer: 4s

Step-by-step explanation: 10s-8s=2s, 2s+2s=4s

Step-by-step explanation:

s =1/4 hope ut may help u

10s-8s+2s =0

12s-8s =0

4 s =0

s =1/4

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