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Frequency (number) of individual claims in each period, XE {0, 1, 2}, follow the binomial distribution (2, 0) and 0 follow distribution U(0, 1). Prediction of the frequency of claims in future periods using the Buhlmann. method c- ZR+ (- Z)H, Z = credibility factor, R = current observation, and H= prior mean process. a) Calculate E(0), E(0) and Var(0) b) Specify E(X0) and Var(X|0) c) Calculate the expected process variance E. Var. (x)) and the conditional mean variance Var (E. (X))) d) Calculate the ratio of the expected process variance to the E. (Var (X 8)) conditional mean variance, *= Vary (E (X 8))

Frequency (number) of individual claims in each period, XE {0, 1, 2}, follow the binomial distribution (2, 0) and 0 follow distribution U(0, 1). Prediction of the frequency of claims in future periods using the Buhlmann. method c- ZR+ (- Z)H, Z = credibility factor, R = current observation, and H= prior mean process. a) Calculate E(0), E(0) and Var(0) b) Specify E(X0) and Var(X|0) c) Calculate the expected process variance E. Var. (x)) and the conditional mean variance Var (E. (X))) d) Calculate the ratio of the expected process variance to the E. (Var (X 8)) conditional mean variance, *= Vary (E (X 8))

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.4: Expected Value
Problem 20E
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Buhlmann's method
Frequency (number) of individual claims in each period, X € {0, 1, 2}, follow the binomial distribution (2, 0) and 0 follow distribution U(0, 1). Prediction of the frequency of claims in future periods using the Buhlmann. method c- ZR+ (- Z)H, Z = credibility factor, R = current observation, and H= prior mean process. a) Calculate E(0), E(0) and Var(0) b) Specify E(XO) and Var(X|0) c) Calculate the expected process variance E. Car, (x)) and the conditional mean variance Var; (E. (X))) d) Calculate the ratio of the expected process variance to the E. (Var (X 8)) conditional mean variance, k- Var, (E. (X 8)) e) Calculate the predicted number of claims in the second period if there are three claims in the first period, E(X₂X₁= 3).
Transcribed Image Text:Frequency (number) of individual claims in each period, X € {0, 1, 2}, follow the binomial distribution (2, 0) and 0 follow distribution U(0, 1). Prediction of the frequency of claims in future periods using the Buhlmann. method c- ZR+ (- Z)H, Z = credibility factor, R = current observation, and H= prior mean process. a) Calculate E(0), E(0) and Var(0) b) Specify E(XO) and Var(X|0) c) Calculate the expected process variance E. Car, (x)) and the conditional mean variance Var; (E. (X))) d) Calculate the ratio of the expected process variance to the E. (Var (X 8)) conditional mean variance, k- Var, (E. (X 8)) e) Calculate the predicted number of claims in the second period if there are three claims in the first period, E(X₂X₁= 3).
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