Problem 2 (Random walk in Z² and Z³)a We consider the uniform random walk on Z². Show that the probability to return at the startingplace after 2n steps is given by p2n = 42 (2) Σko (2)². (hint: use multinomial coefficient to countall the ways to come back in 2n steps)b (bonus) Show that Σo (2)² = (²n).c Use the previous results to show that the walk is recurrent.d We now consider the uniform random walk on Z³, which is transient (as mentioned in class).Read and run the notebook for week 3, also available at this link, to obtain an empirical histogramof the number of visits in (0, 0, 0). Report the values obtained and use them to get an estimate ofthe probability of return P(X; = 0 for some i > 0|Xo = 0).

Answered: Image /qna-images/answer/eea28feb-273b-4ddf-8636-77f996f35085.jpg

Answered: the ways to come back in 2n steps)…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 2EQ: 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed...

See similar textbooks

Similar questions

2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1
Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
What is the simple random walk on integers? Does it always return to the origin if p = ½ ? if p ≠ ½?
a man is investigating the populaion of bear in two areas. Area 1 and Area 2. He expect the number of bear to be X and Y in area 1 and area 2 to be Poisson- distributeted. He expect the number og bear to be λ1 = 3 in area 1 and λ2 = 5 in area 2. Find P(X = 2) and P(X ≥3) and find an approximate value expression for P(X = Y)
During our morning commute we encounter two traffic lights which are distant from one another and may be assumed to operate independently. There is a 50% chance that we will have to stop at thw first of the lights and there is a 30% chance that we'll be stopped by the second light. Find the probabilioty that we are stopped by at least one of the lights.
CONDITIONAL AND MARGINAL PROBABILITY - Statistics and probability } 1) In a plant, complex components are assembled on two different assembly lines, A and B. Line A uses older equipment than B, so it is a bit slower and less reliable. Suppose that on a given day line A assembles 8 components, of which 2 have been identified as defective (D) and 6 as non-defective (ND), while B has produced 1 defective and 9 non-defective components. . a) What is the probability that, when selecting a component at random, a defective one will come out? b) If the selected component is defective, what is the probability that it has left line A? What is the probability that it came out of line B?
What are the lower bound and upper bound of the given problem 1c? Is it 0 or 1? P(x is 40 or fewer senior) = binomcdf (n=50, p=0.72, LB=?, UB=?) = 0.9260
Show that for the simple random walk starting at zero,P(first visit to S^(2n) occurs at t = 2k) = P(S_(2k) = 0) · P(S_(2n−2k) = 0)for 0 ≤ k ≤ n.
How to solve this with cohens d using Microsoft Excel Use alpha of 0.05 2 tail. Free Association (in seconds) Partially Controlled (in seconds)5.84 4.844.64 5.643.56 8.565.00 7.002.35 4.353.67 4.677.87 6.677.74 5.444.48 5.586.56 6.26
Problem 1 One of the advantages that concrete structures have over steel structures is fire resistance (which is to say, steel becomes weak when heated). The time, T, that it takes a steel girder to reach certain temperature (where its strength becomes too low to support its load) in a fire is, however, random. Suppose that for design code development, the following data have been gathered on the time T in hours: 0.736, 0.863, 0.865, 0.913, 0.915, 0.937, 0.983, 1.007, 1.011, 1.064, 1.109, 1.132, 1.140, 1.153, 1.253, 1.394 (a) Compute the values of the sample mean and the sample median by hand. (b) By how much could the smallest sample observation be increased without affecting the value of the sample median? (c) By how much could the smallest sample observation be increased without affecting the value of the sample mean? (d) Compute the values of the first quartile, third quartile, interquartile range, lower fence
Resistors labeled as 100 Ω are purchased from two different vendors. The specification for this type of resistor is that its actual resistance be within 5% of its labeled resistance. In a sample of 180 resistors from vendor A, 150 of them met the specification. In a sample of 270 resistors purchased from vendor B, 233 of them met the specification. Vendor A is the current supplier, but if the data demonstrate convincingly that a greater proportion of the resistors from vendor B meet the specification, a change will be made. a) State the appropriate null and alternate hypotheses. b) Find the P-value. c) Should a change be made?
Resistors labeled as 100 Ω are purchased from two different vendors. The specification for this type of resistor is that its actual resistance be within 5% of its labeled resistance. In a sample of 180 resistors from vendor A, 149 of them met the specification. In a sample of 270 resistors purchased from vendor B, 233 of them met the specification. Vendor A is the current supplier, but if the data demonstrate convincingly that a greater proportion of the resistors from vendor B meet the specification, a change will be made. P-value?

SEE MORE QUESTIONS

Recommended textbooks for you

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Trigonometry (MindTap Course List)

Trigonometry

ISBN:

9781337278461

Author:

Ron Larson

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Trigonometry (MindTap Course List)

Trigonometry

ISBN:

9781337278461

Author:

Ron Larson

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS