a 2. A Consider the "Running in Hot Weather question of PISA 2015 Test (you may find at https://www.oecd.org/pisa/test/p

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A 2 A Consider The Running In Hot Weather Question Of Pisa 2015 Test You May Find At Https Www Oecd Org Pisa Test P 1 (92 KiB) Viewed 90 times

a 2. A Consider the "Running in Hot Weather question of PISA 2015 Test (you may find at https://www.oecd.org/pisa/test/pisa2015/#d.en 537240). An indiviual simulation is done by setting CONDITIONS (Air Temperature (°C), Air Humidity (%) and Drinking Water options) and calculating RESULTS (Sweat Volume (Litres), Water Loss (%) and Body Temperature (°C)). Each simulation is for an one-hour run, call it as RUN PHASE. For example, a RUN PHASE under CONDITIONS (30°C, 40%, NO) will give RESULTS (1.2 Litres, 1.8%,39.3°C). The runner completes a RUN PHASE under initial state conditions, so W.L.L. the above example, our runner will sweat 1.2 liters at the end of first hour. Assume there are several RUN PHASES and our runner drinks water all the time (so that she does not die due to dehydration). The CONDITIONS without Drinking Water option (since it is set as YES) define a STATE. The distance of a state from another state is defined by the total steps between Air Temperature (°C) and Air Humidity (%). For example, (30°C, 40%) has no distance to itself, has a distance of I to (25°C, 40%), has a distance of 3 to 40°C, 20%), etc. There is a transtion between consecutive RUN PHASES and the transition probability between those is defined over the distance between the states. For zero distance, transition probability is Pi i and it is defined for another state j as Pujare, where di is the distance between states i and j. (a) (6 points) Model this problem as a Markov Chain. Define all the states clearly and calculate the whole transition probability matrix P. (b) (8 points) Given that the runner starts at Air Temperature= 35°C and Air Humidity=20%, calculate the expected amount of sweat volume after 3 hours run. Usen-step transition probability matrices for your calculations. (c) (8 points) Given that the runner starts at Air Temperature= 35°C and Air Humidity=20%, calculate the expected amount of water loss after 3 hours run. Use n-step transition probability matrices for your calculations. (d) (8 points) I think that the weather conditions will be Air Temperature= 25°C and Air Humidity -40% with probability 0.35, 30°C and 40% with probability 0.15, 20°C and 40% with 0.10,25°C and 20% with 0.25 and 25°C and 60% with 0.15 for the first RUN PHASE; calculate the expected amount of sweat volume after 3 hours run tomorrow. Use n-step transition probability matrices for your calculations. Assume that our runner will NOT drink water anymore. In this case, when dehydration occurs, our runner cannot recover immediately, stop running and drink some water for not to die, but not run anymore. Also consider if total water loss is above 2.6%, it is EXTREME DEHYDRATION and the runner should be taken to hospital immediately. (e) (6 points) Model this problem as a Markov Chain. Define all the states clearly and calculate the whole transition probability matrix P. (1) (8 points) Given that the runner starts at Air Temperature= 20°C and Air Humidity=20%, calculate the expected number of RUN PHASES under Air Temperature 30°C and Air Humidity=60%. (g) (8 points) Given that the runner starts at Air Temperature= 30°C and Air Humidity=60%, calculate the expected total time to run. (h) (8 points) What is the probability that the runner will be taken to hospital, given that the runner starts at Air Temperature=30°C and Air Humidity=20%?