A gambler has Rs 2/-. He bets Re. 1 at a time and wins Re. 1 with probability1/2. He stops playing if he loses Rs 2 or wins Rs. 4 (a) What is the tpm of therelated Markov chain? (b) What is the probability that he has lost his money atthe end of 5 plays? (c) What is the probability that the game lasts more than7 plays?

Answered: Image /qna-images/answer/fee46331-bdfd-43e2-be94-8ff686f79352.jpg

Answered: A gambler has Rs 2/-. He bets Re. 1 at…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 31E

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If a game gives payoffs of $10 and $100 with probabilities 0.9 and 0.1, respectively, then the expected value of this game is E=0.9+0.1= .
How many DAGS are Markov equivalent to the “chain DAG" X1 → X2 → · .. → X, (excluding itself)?
the map below shows a one-way subway system starting from station 1. A passenger can go from each station to others with equal probability. so a passenger from station 1 can go any other station with probability of 1/4 since there are 14 remaining stationss. a passenger from station 11 can go to any of the remaining stations (12-15) with probability 1/4. what is the probability transition matrix?
Nick takes half-court shots on a basketball court. He is a streaky shooter, so his shot outcomes are not independent. If Nick made his last shot, then he makes his current one with probability a. If Nick missed his last shot, then he makes his current one with probability b, where b < a. Modeling Nick’s sequence of half-court shot outcomes as a Markov chain, what is the long-run probability that he makes a half-court shot?
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13) THE MARKOV CHAIN EXPERIMENT DESCRIBED BELOW HAS TWO STATES: USING A CREDIT CARD AND NOT USING A CREDIT CARD. Hard HT A. GIVEN THE FIRST MONTH FIND THE PROBABILITIES FOR THE THIRD MONTH. P = Given month Card used Card not used B. FIND THE STEADY STABILIZE. Next month: Uses card .8 83 1.3 Card is not used (6 POINTS 14) GIV .2 7 Pr(a woman used a charge card) = .9 Pr(a woman did not use a charge card) = .1 A = [91] 211A STATE VECTOR WHERE THE PROBABILITIES
A certain Mobile Money Agency is an agent for Zanaco Express, Airtel, MTN and Zamtel Mobile Money. Experience has shown that the probabilities of finding a float for withdrawals of amounts K5000 and above are given as 0.4, 0.5, 0.3 and 0.2, respectively. Experience has also shown that among his clients, the probabilities that a client requires a service from Zanaco Express, Airtel, MTN, Zamtel Mobile Money are given as 0.3, 0.4, 0.2 and 0.1, respectively. Assume that each client visits the agency for withdrawals from only one at a time.(i) What is the probability that a client who wishes to withdraw K5000 will not be successful?(ii) What is the probability that an MTN client who wishes to withdraw K5000 will not be successful?(iii) What is the probability that an Airtel client who wishes to withdraw K5000 will not be successful?(iv) A certain client has just failed to make a withdrawal of K7000, what is the probability that he/she is a Zamtel Mobile money client?
There is a 30% chance that any current client of company A will switch to company B this year. There is a 20% chance that any client of company B will switch to company A this year. If these probabilities are stable over the years, and if company A has 1000 clients and company B has 1000 clients, how many clients will each company have in each of the next two years?
A rat is put into compartment 3 of a maze and moves through the compartments at random. The experiment is stopped once the rat reaches compartment 1 or 5. 5 Food 4 3 1 Shock 2 (a) Find the transition probability matrix. (b) What is the probability that the rat finds the food in compartment before the electric shock in compartment ? Use the first-step analysis 1 (c) What is the average time until the experiment is stopped? 5
The purchase patterns for two brands of toothpaste can be expressed as a Markov process with the following transition probabilities. From Special B MDA Need Help? Special B 0.90 = π 1 1/5 π2 1/5 Read It To 0.02 MDA (a) Which brand appears to have the most loyal customers? Explain. MDA ✔✔✔has the most loyal customers because 98 0.10 % stay with them and only 2 (b) What are the projected market shares for the two brands? (Enter exact numbers as integers, fractions, or decimals.) Special B MDA 0.98 X x % switch to the other brand, as opposed to Special B✔✔✔ where only 90 ✓ % stay with them and 10 ✓ % switch.
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