Laserfiche WebLink
<br />3 <br /> <br />o <br />01. WHITE RIVER R,S, and W <br />00 <br /><.0. The second major simplification of this method is defining R, S and <br />W as discrete random variables allowing only a small number of possible <br /> <br />outcomes. These outcomes can be called inflow intervals, conditions or <br /> <br />states, like low, mediwn and high inflows. For the White River, let us <br />define the inflows R by the following distribution with four outcomes <br />(flows are given as thousands of acre-feet in this and all subsequent <br /> <br />formulae and tables): <br /> <br /> Pr [R = 53.5] = .131 <br /> Pr [R = 81.3] = .478 <br /> Pr [R= 111,9] = .304 <br /> Pr [R = 151. 0] = .087 <br />The swn of these probabilities is one. The expected value of R is E[R] = 93, <br /> <br />that is, the mean inflow during April, May and June is 93,000 acre-feet <br />per month, The R outcomes are estimated as the sample means in the inflow <br />intervals while the probabilities are the proportion of observations in <br />each interval from the 69 years of estimated natural inflows which have <br /> <br />been developed by the U.S, Bureau of Reclamation (USBR). The overall mean <br /> <br />of 93,000 acre-feet also is exact. However, the standard deviation of <br /> <br />this empirical R distribution is necessarily less than the true standard <br />deviation due to the grouping in intervals. <br /> <br />The S,R joint distribution is as follows: <br />Pr [S = 19,8, R = 53.5] = .029 <br />Pr [S = 33, R= 53.5] = .102 <br />Pr [S = 28.2, R = 81. 3] = ,145 <br />Pr [S = 40, R = 81.3] = .333 <br />