2: One way to measure species diversity is to use the Shannon diversity index H. If a habitat consists of three species, A, B, and C, then its Shannon diversity index is H = 9:ln.r ylny zlnz, where :1: is the percent of species A in the habitat, y is the percent of species B in the habitat, and z is the percent of species C in the habitat. Use the fact that a: + y + z = 1 to show that the maximum value of H occurs when :1: = y 2 z 2 1/3. What is the maximum value of H