Please solve while showing the steps clearly

The Gamma distribution with mean p and variance u'/o has density function (> > 0) u"T(u) (a) Show that this may be written in the form of an exponential family. (b) Use the properties of exponential families to confirm that the mean and variance of the distribution are u and p jo. [9] (ii) Explain the difference between a continuous covariate and a factor. (tii) A company is analysing its claims data on a portfolio of motor policies, and uses a gamma distribution to model the claim severities. The company uses three rating factors: policyholder age (as a continuous variable): policyholder gender; vehicle rating group (as a factor) (a) Write down the form of the linear predictor when all rating factors are included as main effects. (b) State how the linear predictor changes if an interaction between policyholder age and gender is included. 141 [Total 16]