{"id":33919,"date":"2018-02-20T23:50:30","date_gmt":"2018-02-20T23:50:30","guid":{"rendered":"https:\/\/writemyessayfree.com\/probability-markov-chains"},"modified":"2017-08-16T06:22:13","modified_gmt":"2017-08-16T06:22:13","slug":"probability-markov-chains","status":"publish","type":"post","link":"https:\/\/www.benedictsol.com\/blogs\/probability-markov-chains\/","title":{"rendered":"Probability \u2013 Markov chains"},"content":{"rendered":"<div class=\"the_content_wrapper\">\n<p>Probability \u2013 Markov chains<\/p>\n<p>Markov Chains First assignment<br \/> Solutions should be handed in in one pdf document, well-written and readable. Elucidate the line of thought by plain English \u2013 so not only formulas!<br \/> Exercise 1 \u2013 Olinick 7<br \/> A particle moves along a line from an initial position 2 feet to the right of the origin. Each minute it moves one foot to the right with probability 1\/2 or 1 foot to<br \/> the left. There are barriers at the origin and 4 feet to the right of the origin; if the particle reaches the barrier at the origin, it must move one foot to the right<br \/> in the next minute, while if it hits the other barrier, it must move one foot to the left in the next minute. Determine the transition matrix for the associated Markov<br \/> chain and draw the state diagram.<br \/> Exercise 2<br \/> Assume that a persons work can be classified as professional, skilled labor, or unskilled labor. Assume that of the children of professionals, 80% are professional,<br \/> 10% are skilled laborers, and 10% are unskilled laborers. In the case of children of skilled laborers, 60% are skilled laborers, 20% are professionals, and 20% are<br \/> unskilled laborers. Finally, in the case of unskilled laborers, 50% of the children are unskilled laborers, and 25% each are in the other two categories. Assume that<br \/> every person has a child, and form a Markov chain by following a given family through several generations. In commenting on the society described, the famed<br \/> sociologist Harry Perlstadt has written, \u201dNo matter what the initial distribution of the labor force is, in the long run the majority of the workers will be<br \/> professionals\u201d. Is he correct? Why?<br \/> Exercise 3 \u2013 drunken walk<br \/> In a busy street, there are three bars next to each other. Bar 1 one is next to bar 2, which is in the middle, so bar 3 is on the other side of bar 2. A man goes for a<br \/> drink, and after each drink he randomly chooses with equal probabilities to either stay and have another drink at the same bar, or go outside and chooses a<br \/> neighbouring bar to have a drink.<br \/> 1. What is the long-term probability that he is in each of the bars?<br \/> 2. Supposethepriceofadrinkinbar1is 1,inbar2itis2,andinbar3youcan get a drink for 3. Suppose the man starts in bar 1. What is the expected amount of money spent,<br \/> if the man decides to have 4 drinks?<br \/> The city council has decided to fight the abuse of drinking. So they built a jail next to bar 1, and a detox clinic next to bar 3. To be precise, the street now<br \/> contains a row of five buildings: a jail, bar 1, bar 2, bar 3, and the detox clinic. Furthermore, they decided that after one drink in a bar, each visitor must get<br \/> out, and there should be no more cheap bars: all prices become equal to 3. One night the same man enters one of the bars, and after having a drink, he randomly selects<br \/> one of the neighbouring buildings to enter. If that is the jail or the detox clinic, he has to stay there.<br \/> 3. Suppose the man has again money for four drinks. What is the probability that he ends in jail?<br \/> 4. Suppose he starts in bar 1, and he has endless money. What is the probability that he ends in jail?<br \/> 5. Suppose he has endless money. How many drinks will he have had before he ends up in jail or detox? Does it matter in which bar he started?<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Probability \u2013 Markov chains Markov Chains First assignment Solutions should be handed in in one pdf document, well-written and readable. Elucidate the line of thought by plain English \u2013 so not only formulas! Exercise 1 \u2013 Olinick 7 A particle <a href=\"https:\/\/www.benedictsol.com\/blogs\/probability-markov-chains\/\" class=\"read-more\">Read More &#8230;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-33919","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/33919","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/comments?post=33919"}],"version-history":[{"count":0,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/33919\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/media?parent=33919"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/categories?post=33919"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/tags?post=33919"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}