HI im not sure about this question. Can you help me to solve this ? Thanks!

1. The Parcto probability distribution has many applications in economics, biology, and physics. Let B >0 and 6 > 0 be population parameters, and X . X2. ...,X, be a random sample from a distribution with probability density function A(x: B.6) = 8-86 x>B. zero otherwise. Suppose B is known. a) (6) Show that W = In = In X - InB follows an Exponential distribution. What is the mean 0 of this exponential distribution? No credit will be given without proper justification- b) (3) Find the sufficient statistic w ( X] , X2, ..., X,; ) for 5. c) (9) (i) Obtain the maximum likelihood estimator of 8, 8. (ii) Suppose 1=6, B=5, and x =5.65, x2=6.50, x3 = 7.50, x4 = 8.85, x5 = 10.30, x = 12.50. Find the maximum likelihood estimate of 6. d) (7) Is the maximum likelihood estimator & an unbiased estimator of 6? If & is not an unbiased estimator of o, construct an unbiased estimator of & based on a- e) (10) (i) Suggest a confidence interval for & with (1 - a ) 100 % confidence level. (ii) Suppose #7=6, B=5, and x =5.65, x, =6.50, x} = 7.50, x = 8.85, x5= 10.30, x = 12.50. Construct a 95% confidence interval for 6. Hint: Use IM= W IM= In Xi B1. ( continued ) f) (8) Assume 63 1. (i) Obtain a method of moments estimator of 6, 8. (ii) Suppose 1=6, B=5, and x] =5.65, X2=6.50, X3 =7.50, x=8.85, X5= 10.30, X = 12.50. Find a method of moments estimate of &. g) (5) Assume 6 3 1. Is the method of moments estimator of 8, 8 , an unbiased estimator of 6? If & is not an unbiased estimator of 6, does & underestimate of overclimate o ( on average )