Let us have the experience of a mouse falling into a trapinside a 6-room building, as shown in the figure below. Ifthe room contains k doors, the probability that the mousewill choose one of these doors is 1/k if the mouse reachesroom F that contains the food or room S that contains thetrap. It will stay there and the experiment ends, thetransition matrix isM=[0.5 00.5 00.300¹0.50 0 0.3 0.300.3 0.30 0.5 0000O aO bО с2000 0.50 0.5 0 000 0.30 0.50 0.5M =-00.50.5b3..+.4500SM=00 0100.5 0 0000.5 0 00.3 0.3 0 0 0.30 0.5 0 0 0.5001 0000010 0 0000.5 0 0 0.5 00.30 0.3 0.300.3 0.3 0 00 0.5 0 0000 0000C000.30.51(a)

Given the experience of a mouse falling into a trap inside a 6-room building, as given in the…

Answered: Let us have the experience of a mouse…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

If possible, fill in the missing values to make A a doubly stochastic matrix. (If not possible, enter IMPOSSIBLE.) - [ 0.3 a = b = A = a 0.3 X X
What is the second row of the matrix A, if A is stochastic? Second row: 0.8 The steady state vector for A is If v= 0.5 [15] 26 then Av approaches as n gets large. A = [0.2 ? 0.5] ?
Question 6
At any age, about 20% of American adults participate in physical conditioning activities at least twice a week. However, these activities change as people get older, and occasionally participants cease to be older as they age. In a local survey of n = 100 adults over 40 years of age, a total of 15 people indicated that they participated in these activities at least twice a week. Does this data indicate that the percentage of participation for adults over 40 years of age is considerably less than the 20% figure? Find the p-value and use it to draw the appropriate conclusions.
Answer all parts of question 3
Find the probability of going from state A to state B in two trials, given the transition matrix P and the second power of P below. A B с 0.5 0.3 0.2 0.2 0.2 0.6 0.1 0.7 0.2 ΑΓ P=B A and p² B C A B C 0.33 0.35 0.32 0.20 0.52 0.28 0.21 0.31 0.48 The probability of going from state A to state B in two trials is DE
Example 7.40: You set out on a walk with three possible locations, denoted locations 1, 2 and 3. The probabilities of travelling from a specified location to the next are given by Solution. If you know that you started in location 3, what is the probability that you end up at location 1 after two time periods? Using the above equation, we get To solve this we use the equation Xn+1 = AXn. Given that you began in location 3, the initial state vector is and subsequently Exercise X₁ = AX0 Probability = A = = X₂ = AX₁ 0.5 0.2 0.4 0.4 0.6 0.1 0.1 0.2 0.5 = Xo 0 0.5 0.2 0.4 0.4 0.6 0.1 0.2 0.5 0.1 ][ Therefore the probability of ending up in location 1 after two time periods is 0.42. 0.5 0.2 0.4 0.4 0.6 0.1 0.1 0.2 0.5 1 0.4 0.1 = 0.5 0.4 0.1 0.5 = 0.42 0.27 0.31 Refer to the example above. If you know that you started in location 2, what is the probability that you will end up at location 1 after one time period?

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS