Four-week summer rainfall totals in a certain section of themidwestern United States have a relative frequency histogram thatappears to fit closely to a gamma distribution with a = 1.6 and B =2.0.

a)

Find an interval that will include the rainfall total for aselected 4-week period with a probability of at least 0.75.

Can we use This rule without using Tchebysheff’s theorem ?.

The Gamma Distribution -X/B е T(a)pa? = x > 0 f(x) = elsewhere E(X) = aß and V(X) = aß2 a, ß > 0 The parameters a and ß determine the specific shape of the curve. Some typical gamma densities are shown in Figure 6.12. As described in the previous section, the function I(a) known as the gamma function is defined by T(a) 1 x-1€ *dx, a 21 Some useful results: T(a + 1) = al(a) T(n) = (n − 1)! for any positive integer n O . T(1/2) = V