Kkindly address the following questions fully. Be precise

An insurance company is investigating past data for two household claims assessors, A and B, used by the company. In particular claims resulting from similar types of water damage were extracted. The following table shows the assessors' initial estimates of the cost (in units of (100) of meeting cach claim. A: 4.6 6.6 2.8 5.8 2.1 5.2 5.9 34 7.8 3.5 1.6 8.6 2.7 B: 5.7 34 4.7 3.6 6.5 3.3 3.8 2.4 7.0 4.0 4.4 for the A data: " = 13, Ex = 60.6 and Er2 = 340.92 for the A data: " = 11, Er = 48.8 and Er2 = 236.80) (1) Draw a suitable diagram to represent these data so that the initial estimates of the two assessors can be compared. [2] (ii) You are required to perform an appropriate test to compare the means of the assessors" initial estimates for this type of water damage. (a) State your hypotheses clearly. (b) Use your diagram in part (i) to comment briefly on the validity of your test. (9) Calculate your test statistic and specify the resulting P-value. (d) State your conclusion clearly. [10] (iii) You are required to perform an appropriate test to compare the variances of the assessors' initial estimates. (a) State your hypotheses clearly. (b) Use your diagramn in part (i) to comment briefly on the validity of your test. Calculate your test statistic and specify the resulting P-value. (d) State your conclusion clearly and hence comment further on the validity of your test in part (ii). [7] (iv) Use your answers in parts (i) to (iii) to comment on the overall comparison of the two assessors as regards their initial estimates for this type of water damage. [1] [Total 20]An investor is contemplating an investment with a payoff of R, where R has the probability density function f, given by: At) - 0 :1