A regular octagonal spinner is made up of eight isosceles triangles. Two of the triangles have a score of 2, three triangles have a score of 'a' and three triangles have a score of ‘b’, where a < b. The expectation and variance of the spinner are given by:

E(X) = 4.25

Var(X) = 75/16

a. Find an expression for G_x(t), G'_x(t) and Gⁿ_x,(t).

b. Hence, find the values of a and b.