Kindly provide answers for the following quiz

If individual claim amounts X follow a lognormal distribution with PDF: 2 fx ( x ) =- log x - H exp X30 derive a formula for the average claim amount.A random sample of 100 claim amounts M,x,...., Mon is observed from a Weibull distribution with parameter y = 2, where a is unknown. For these data: Er, = 487, 926 Ex- = 976,444,000 median = 4,500 (i) (a) Show that the maximum likelihood estimator for c is given by: 8 =n (b) Hence estimate the value of c. [4] (ii) Estimate the value of e using the method of moments. (2] (iii) Calculate the method of percentiles estimate of c. [2] [Total 8]A random sample of 100 claim amounts M,x,...., Mon is observed from a Weibull distribution with parameter y = 2, where a is unknown. For these data: Er, = 487, 926 Ex- = 976,444,000 median = 4,500 (i) (a) Show that the maximum likelihood estimator for c is given by: 8 =n (b) Hence estimate the value of c. [4] (ii) Estimate the value of e using the method of moments. (2] (iii) Calculate the method of percentiles estimate of c. [2] [Total 8]