In the study of a storage dam design, it is assumed that quantities can be measured...

In the study of a storage dam design, it is assumed that quantities can be measured sufficiently accurately in units of ¼ of the dam’s capacity. It is known from past studies that at the beginning of the first (fiscal) year the dam will be either full, ¾ full, ½ full, or ¼ full, with probabilities 1/3, 1/3, 1/6, and 1/6, respectively. During each year water is released. The amount released is ½ the capacity if at least this much is available; it is all that remains if this is less than ½ the capacity. After release, the inflow from the surrounding watershed is obtained. It is either ½ or ¼ of the dam’s capacity with probabilities 2/3 and 1/3, respectively. Inflow causing a total in excess of the capacity is spilled. Assuming independence of annual inflows, what is the probability distribution of the total amount of water at the beginning of the third year? Use total probability theorem.

Expert Solution

Y3 denotes the probability distribution of the total amount of water at the beginning of the third year.

milcah answered 1 year ago

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