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Show that the differential equation of Exercise 30 with b = c = 0 and a > 0 yields a normal distribution.
Exercise 30
Karl Pearson, one of the founders of modern statistics, showed that the differential equation
yields (for appropriate values of the constants a, b, c, and d) most of the important distributions of statistics. Verify that the differential equation gives
(a) the gamma distribution when a = c = 0, b > 0, and d > -b;
(b) the exponential distribution when a = c = d = 0 and b > 0;
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What distribution would seem most appropriate to model the TTR data - If your suggested model were valid what proportion of TTR values is likely to exceed the maximum allowable?
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