f(alpha) exercise 2 solution

For r = 0.5, p1 = 0.05, p2 = 0.2, p3 = 0.3, and p4 = 0.05, the formula

alpha = (log(p1)*p1q + log(p2)*p2q + log(p3)p3q + log(p4)*p4q)/ (log(r)*(p1q + p2q + p3q + p4q))

becomes

alpha(-1) = (Log(.05)*(.05-1) + Log(.2)*(.2-1) + Log(.3)*(.3-1) + Log(.45)*(.45-1))/(Log(.5)*(.05-1 + .2-1 + .3-1 + .45-1)) = 3.48

alpha(1) = -(Log(.05)*(.051) + Log(.2)*(.21) + Log(.3)*(.31) + Log(.45)*(.451))/(Log(.5)*(.051 + .21 + .31 + .451)) = 1.72

alpha(3) = -(Log(.05)*(.053) + Log(.2)*(.23) + Log(.3)*(.33) + Log(.45)*(.453))/(Log(.5)*(.053 + .23 + .33 + .453)) = 1.35

Return to f(alpha) exercise 2.