1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kondaur [170]
3 years ago
10

A particle moves on a circle through points which been marked 0,1,2,3,4 (in a clockwise order). At each step it has a probabilit

y p of moving to the right (clockwise) and 1- p to the left (counterclockwise). Let Xn denote its location on the circle after nth step. The process { Xn, n>= 0} is a Markov Chain a. Find the transition probability matrix. b. Calculate the limiting probabilities.
Mathematics
1 answer:
Sedaia [141]3 years ago
4 0

Answer:

Step-by-step explanation:

Given data:

SS={0,1,2,3,4}

Let probability of moving to the right be = P

Then probability of moving to the left is =1-P

The transition probability matrix is:

\left[\begin{array}{ccccc}1&P&0&0&0\\1-P&1&P&0&0\\0&1-P&1&P&0\\0&0&1-P&1&P\\0&0&0&1-P&1\end{array}\right]

Calculating the limiting probabilities:

π0=π0+Pπ1                 eq(1)

π1=(1-P)π0+π1+Pπ2     eq(2)

π2=(1-P)π1+π2+Pπ3    eq(3)

π3=(1-P)π2+π3+Pπ4    eq(4)

π4=(1-P)π3+π4             eq(5)

π0+π1+π2+π3+π4=1

π0-π0-Pπ1=0

→π1 = 0

substituting value of π1  in eq(2)

(1-P)π0+Pπ2=0

from

π2=(1-P)π1+π2+Pπ3  

we get

(1-P)π1+Pπ3 = 0

from

π3=(1-P)π2+π3+Pπ4

we get

(1-P)π2+Pπ4 =0

from π4=(1-P)π3+π4  

→π3=0

substituting values of π1 and π3 in eq(3)

→π2=0

Now

π0+π1+π2+π3+π4=0

π0+π4=1

π0=0.5

π4=0.5

So limiting probabilities are {0.5,0,0,0,0.5}

You might be interested in
I need help with this ​
ycow [4]

Answer:

it looses 200 in value for the first year

Step-by-step explanation:

I am in middle school first year.I have no idea how to solve this but i hope it helps

5 0
3 years ago
Cos(x)= sin(35) what does x =?
mylen [45]
Here,

cos(x) = sin(35)
cos(x) = cos(90-55)
cos(x) = cos(55)
x = 55
3 0
3 years ago
The equation the quantity of x plus 20 over 2 = 3x represents when two tutoring services with different rate plans charge the sa
Inga [223]

None of the options give the same fees for a session of x hours.

Given,
x + 20/2 = 3x
when two tutoring services with different rate plans charge the same fees for a session of x hours.

<h3>What is arithmetic?</h3>

In mathematics, it deals with numbers of operations according to the statements.

x + 20/2 = 3x
x + 10 = 3x

A) x= 10
10 + 10 = 3*10
20 ≠ 30


B) x=4
4 + 10 = 3 * 4
14 ≠ 12

C) x= -14
-14 + 10 = 3 * -14
-4 ≠ 42


D) x=-17
- 17 + 10 = 3 * - 17
-7 ≠ -51

Here, none of the options give the same fees for a session of x hours.

Thus, none of the options give the same fees for a session of x hours.

Learn more about arithmetic here:

brainly.com/question/14753192

#SPJ1

8 0
1 year ago
A roofer sketches a diagram of a house on which he is working.
docker41 [41]
Using the SSA formula:

X = SQRT ( 40^2 + 26^2 - 2*40*26*cos(65))

X = SQRT(2276 - 2080*cos(65))

X = SQRT(1396.954)

X = 37.37 = 37.4 ft.
4 0
4 years ago
Read 2 more answers
Ehich of thr following expressions has a Simplified value of 3A -2?
LenaWriter [7]
The answer is B. -a+4+5a-a-6

3 0
3 years ago
Other questions:
  • Shayla has 5 pets which is 3 more than half the number of pets Judy has. how many pets does Judy have
    11·2 answers
  • Your friend Bob makes a triangle out of a pen, a pencil, a small ruler. Using the same three school supplies, you try to make a
    15·1 answer
  • The first decision is a choice between y = acos[b(x – h)] + k and y = asin[b(x – h)] + k. Starting at the green point, which gen
    14·2 answers
  • What algebraic expression represents GK, if GK =37, what are GH and JK. GJ=4x+2 and HK=6x-1
    5·1 answer
  • A number m plus six times m
    13·1 answer
  • Can you answer this?
    13·1 answer
  • The two box-and-whisker plots below represent the distribution of shoe sizes for a group of 40 two-year-old boys and a group of
    8·1 answer
  • How much more than 1/4 cup is 3/4 cup?
    11·2 answers
  • A survey of 1100 adults from a certain region​ asked, "If purchasing a used car made certain upgrades or features more​ affordab
    8·1 answer
  • Can someone help me with this question? Thank you!
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!