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please to refer to the question in tThe amount of stored water in a reservoir may be idealized into three states: full (F), half-full (H), and empty (E). Because of the probabilistic nature of the inflowing water into the reservoir, as well as the outflow from the reservoir to meet uncertain demand for water, the amount of water stored may shift from one state to another during each season. Suppose that these transitional probabilities from one state to another are as indicated in the figure below. For example, in the beginning of a season, if the water storage is empty, the probability that it will become half-full at the end of the season is 0.5 and the probability that it will remain empty is 0.4 and son on. Assume that the water level is full at the start of the season. - What is the probability that the reservoir will be full at the end of one season? What is the probability that the reservoir will contain water at the end of one season? - What is the probability that the reservoir will be full at the end of the second season? What is the probability that the reservoir will contain water at the end of the second season? 0.1 0.4 Half-Ful 0.7 0.4 0.3 0.2 0.Ihe image

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The transition probability for F -F is 0.2. This is the probability of the reservoir being fill after one transition F E 0.1 So prob of reservoir being empty 0.1 Prob of being non-empty 1 - probe of being empty 1 - 0.1 0.9 The 2 step transition probabilities are: FFF, F>HF, FEF Prob of FF-> F 0.2 0.2 0.04 Prob of F->H-> F 0.7 * 0.4 0.28 Prob of F->E->F 0.1 *0.1 0.01 Sum of all 3 prob 0.33First find the 2-step transition prob from F to E The cases are FFE,FEE, F H E Prob of F->F->E 0.2*0.1 0.02 Prob of F-> E-> E 0.1 * 0.4 0.04 Prob of F->H->E 0.70.5 0.35 The sum of all three cases 0.41 This is the 2-step probability of no water in reservoir 0.41 So, 2 step probability of water in reservoir 1 0.41 0.59

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