Question: Basic statistics for the collective risk model. An actuary has analysed company Xs motor third-party liability losses for next year by modelling the number of

Basic statistics for the collective risk model. An actuary has analysed company X’s motor third-party liability losses for next year by modelling the number of losses as a negative binomial distribution with rate equal to 208.8 and a variance-to-mean ratio of 2.5, and the severity of losses as a lognormal distribution with μ = 10.5 and

σ = 1.3. Calculate the expected aggregate losses and the standard deviation of the aggregate losses for next year.

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