Karl Pearson, one of the founders of modern statistics, showed that the differential equation Yields (for appropriate

Question:

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;
(c) The beta distribution when a = 0, b = €“ c, d€“ 1 / b €“ 1.

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...