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+Q- Z)H, Z = credibility factor, R = current observation, and H= prior mean process. a) Calculate E(0), E(02²) and Var(0) b) Specify E(X 0) and Var(X 0) c) Calculate the expected process variance E. (Var, (x)) and the conditional mean variance Var, (E. (Xe)) d) Calculate the ratio of the expected process variance to the E.(Var, (X 8)) conditional mean variance, *- 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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Please answer number 3
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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