Problem 3. (Influentials and Imitators) Suppose that potential adopters of a given product fall into two distinct segments: influentials and imitators. Each segment has its own withinsegment innovation and imitation parameters and experiences its own Bass-type contagion process. In addition, the influentials can exert a cross-segment influence on the imitators, but not vice-versa. Let denote the proportion of influentials in the population of eventual adopters (01), and =1 denote the proportion of imitators. Let pi and qi denote the within-segment innovation and imitation parameters, respectively, for i=1,2, where i=1 represents influentials and i=2 represents imitators. Let qc denote the cross-segment imitation parameter. a) Write a formula expressing each segment's instantaneous adoption behavior (in analogous to d(t)=(p+mqD(t))(mD(t))). b) What is special about the case in which =0 or =1 ? c) If there are no pre-release purchases (i.e., D1(0)=D2(0)=0 ), write a formula expressing the cumulative adoption at time t (in analogous to D(t)=m1+pqe(p+q)t1e(p+q)t)