On each day t of n days, N customers of a supermarket were sampled and the number Xt expressing dissatisfaction was recorded. The results suggested that there were good and bad days for customer satisfaction.

(a) What kind of results might have led to this conclusion?

(b) What kind of model of Xt might be used?

(c) Derive expressions for the mean and variance of Xt under this model?

(d) Write down the likelihood of this model.

(e) What parameter constraints apply to this model?

(f) Suggest a reparameterisation for this model, explaining your reasoning.