Please help solve this problem. Thank you

(i) A random variable X has the lognormal distribution with density function f(x) and parameters / and o. Show that for a > 0: where @ is the cumulative distribution function of the standard normal distribution. [4] (ii) Claims under a particular class of insurance follow a lognormal distribution with mean 9.070 and standard deviation of 10.132 (figures in f(00s). In any one year 20% of policies are expected to give rise to a claim. An insurance company has 200 policies on its books and wishes to take out individual excess of loss reinsurance to cover all the policies in the portfolio. The reinsurer has quoted premiums for two levels of reinsurance as follows (figures in t000s): Retention Limit Premium 25 48.5 30 38.2 (a) Calculate the probability. under each reinsurance arrangement, that a claim arising will involve the reinsurer. (b) By investigating the average amount of cach claim ceded to the reinsurer, calculate which of the retention levels gives the best value for money (ignoring the insurer's attitude to risk). (c) The following year, assuming all other things equal, the insurer believes thiat inflation will increase the mean and standard deviation of the claims in its portfolio by 8%. If the reinsurer charges the same premiums as before, which of the retention levels will be best value for money next year? [18 Total 22]