This is for a Linear Algebra class. Please provide explanations for the answer (3) In the casino game of roulette, a ball is spun around a wheel with 38 slots, 18 of which are colored black. If you bet on black, then you gain a profit of $1 if the ball lands on one of the 18 black slots, but you lose $1 if it lands on one of the other 20 slots (a) Write out the transition matrix for a Markov Chain representing how much money you have in your pocket before and after a single play of roulette assuming that you will start with less than $10 and stop once you get to either $0 or $10. For example, if you have $4 at some point in the night, then you will either have $5 or S3 after the next round depending on whether black comes up or not, but if you get to $0 or $10 at any point, you stop playing (b) Calculate the eigenvalues of your transition matrix and identify all possible sta- tionary distributions. Discuss convergence (unique for any initial? fail to converge? etc. (c) Suppose that you start the night with S5. Calculate the probability that you double your money before losing it all (i.e. probability that you end the night with S10 instead of $0)

Central topic markov chains: Every summer the Yates de los Lagos owners association decides if its annual regatta will be held in June, July or August. If it takes place in June, the probability of good weather is ¾; and if these conditions exist, the regatta of the next year it will be done in June with probability 2/3, in July with probability 1/6 or in August with probability 1/6; but if there is bad weather, next year's regatta will take place in July or August with equal probabilities. If the competition is held in July, good and bad weather have equal probabilities; if there is good weather, the next year's regatta will be held in July; If there is bad weather, the next regatta will take place in August with probability of 2/3 or in June with probability of 1/3. If the regatta takes place in August, the probability of good weather is 2/5; and if there are good conditions atmospheric conditions, next year's regatta will take place in July or August, with equal probabilities; but…

TOPIC: MARKOV CHAINS A housewife always uses one of three brands of detergent: "A", "B" or "C". Which one she buys depends inwhich of the three manufacturers is running a promotional campaign (with gifts such as combs, ornaments, etc.),etc.). Companies undertake such campaigns at random, regardless of whether or not competitors are running other campaigns at the same time.not running other campaigns at the same time. Brand "A" company runs a campaign ½ of the time, brand "B" runs a campaign 1/3 of the time, and brand "B" runs a campaign 1/3 of the time, and brand "C" runs a campaign 1/3 of the time.1/3 of the time, and "C" promotes 1/3 of the time. If the lady buys brand "A" on a certain occasion, the next time she will also buy brand "A".If she buys brand "A" on a certain occasion, the next time she will also buy brand "A", if your company is promoting or if neither of the other two is doing so.or she buys brand "B" if it is on promotion, but brand "A" is not, or she buys brand "C" if…

Show full answers and steps to part d) and e) using Markov Chain Theory. Please explain how you get to the answers without using excel, R or stata