3. Suppose that sixty percent of claims have a normal distri- bution with mean 3000 and variance 10002. The remaining forty percent of claims have a Pareto distribution with pa- rameters 0 = 12000 and a = 4. a) Find the mean and standard deviation of the finite mix- ture.

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3. Suppose that sixty percent of claims have a normal distri-
bution with mean 3000 and variance 1000². The remaining
forty percent of claims have a Pareto distribution with pa-
rameters 0 = 12000 and a = 4.
%3D
a) Find the mean and standard deviation of the finite mix-
ture.
b) Find the probability that a claim exceeds 5000.
Transcribed Image Text:3. Suppose that sixty percent of claims have a normal distri- bution with mean 3000 and variance 1000². The remaining forty percent of claims have a Pareto distribution with pa- rameters 0 = 12000 and a = 4. %3D a) Find the mean and standard deviation of the finite mix- ture. b) Find the probability that a claim exceeds 5000.
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