Q&A Part 5 - Q5.6 parts (ii) & (iii) Mistake?

[f888bet]

I believe that there is an error in the solution to this question.

In part (i) the number of claims for a Poisson frequency under full credibility is 1,920. I fully get this.

In part (ii), the ratio of the variance to mean for frequency is 2, as stated in the question. This corresponds to the 2 in the solution. However, shouldn't the mean for the severity be squared as in part (i), so you get (555.55/33.33^2) and NOT (555.55/33.33) as the solution suggests?

This would tie in with the formula for full credibility for Premiums (general) given on P.57 of the notes in the chapter summary.

My approach gives an answer of 1280*2.5=3200, not 11,947. This seems more sensible given that the solution in (i) is 1,920, and the severity effect has not changed (only the frequency distribution has).

Does anyone have the same issue with the solution to this question? Obviously if this is incorrect, there is a knock-on effect for part (iii).

Regards,

F888BET

 

[Duncan Brydon]

Thank you for pointing this out. Just to avoid confusion for other students reading the forum, I think you are referring to the solution to part (iii) of question 5.6 in the Q&A Bank.

We do indeed need 33.33^2 on the denominator. Well spotted. This gives an answer of 1600 for the number of claims needed to obtain full credibility.

We will issue a correction to this, and part (iv) which is affected as a result as you point out.