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Quiz%201_B

# Quiz%201_B - Name ID 1 A random variable X is assumed to...

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Name: ID: 1. 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 given X = 155 (i.e. say which type of distribution it is and what are the parameters). 2. Suppose that given the random variables X 1 , …, X n are i.i.d. with pf (x j )= (belongs to LEF) Where has pdf ()= Determine the parameters in the resulting posterior distribution. 3. Claim sizes follow the distribution (density function) , are unknown. The following sample of claim sizes is available: 12, 25, 35, 40, 70, 150, 250. Percentile matching at the 50 th percentile is used to estimate. Determine the resulting estimate of 4. Two hundred losses are observed. Three of the losses are 300, 500, 800. All that is known

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Quiz%201_B - Name ID 1 A random variable X is assumed to...

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