Quiz%201_A - Name: ID: 1. The random variable has pdf . It...

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Name: ID: 1. The random variable has pdf . It is known that =1000. You are given the following five observations: 43 145 233 396 775 (sample mean = 318.4). Determine the method-of-moments estimate of . A. <4 B. 4<<4.2 C. 4.2<<4.4 D. 4.4<<4.6 E. >4.6 2. Suppose a sample of 5 losses given by 43, 145, 233, 396 and 775 ( same as question 1 ) is observed. You assume that the pdf for each loss X i , i = 1, … , 5 is given by , x > 0 , and that the losses X i are iid. Determine the MLE for (i.e.). Ɵ A. < 70 B. 70 < < 74 C. 74 < < 78 D. 78 < < 82 E. > 82 3. Assume that (same as question 2) has been calculated, construct the 95% confidence interval using asymptotic normality of A. ± 1.645*0.223624 B. ± 1.96*0.223624 C. ± 1.645*4.47179 D. ± 1.96*4.47179 E. ± 1.645*19.9969 4. A random variable X is assumed to satisfy X|( Θ = ) ~ Pareto ( , β = 1200), and thus Ɵ Ɵ = , x > 0 and the prior distribution for is Exponential with mean 5, i.e. Ɵ , >0. Ɵ Determine the posterior distribution of
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Quiz%201_A - Name: ID: 1. The random variable has pdf . It...

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