再问 2 道 p sample 的题，谢谢大家。

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周六就要考了，还有几题看不明白，谢谢大家了。

129. The cumulative distribution function for health care costs experienced
by a policyholder is modeled by the function
F(x)=1-e^(-x/100)  for x>0,
     0             otherwise.

The policy has a deductible of 20. An insurer reimburses the policyholder
for 100% of health care costs between 20 and 120 less the deductible. Health
care costs above 120 are reimbursed at 50%. Let G be the cumulative
distribution function of reimbursements given that the reimbursement is
positive.
Calculate G(115).

以下是答案。

Key: B
The reimbursement is positive if health care costs are greater than 20, and
because of the memoryless property of the exponential distribution, the
conditional distribution of health care costs greater than 20 is the same as
the unconditional distribution of health carecosts.
We observe that a reimbursement of 115 corresponds to health care costs of
150
(100% x(120 – 20) + 50% x (150 – 120)), which is 130 greater than the
deductible of 20.
Therefore,G(115)=F(130).



我的问题是 为什么 G(115)=F(130).



135. The number of workplace injuries, N, occurring in a factory on any
given day is Poisson distributed with mean λ. The parameter λ is a random
variable that is determined by the level of activity in the factory, and is
uniformly distributed on the interval [0, 3].

Calculate Var (N).
(A) λ
(B) 2 λ
(C) 0.75
(D) 1.50
(E) 2.25

以下是答案。
Key: E
Var (N) = E [ Var ( N | λ )] + Var [ E ( N | λ )] = E (λ) + Var (λ) = 1.
50 + 0.75 = 2.25


我的问题是为什么
Var (N) = E [ Var ( N | λ )] + Var [ E ( N | λ )] = E (λ) + Var (λ)


太感谢大家了，

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关键词：Sample AMPL amp MPL SAM

第一题：
如果你没算对，可能是因为题目没看清楚，题目的问题是given that the reimbursement is positive。根据key的提示，G(115)说明health care costs等于150，但是deductible是20，所以根据指数函数的无记忆性G(115)
=F(150)/(1-F(20))=F(150-20)=F(130)
第二题：
把等式右边根据方差和期望的定义展开，就可以得到右边=E(N^2) - (E(N))^2。其实这道题相当于给出了(N,λ) 的联合分布，让你求N的方差。

magiclys 发表于 2010-1-13 17:31
第一题：
如果你没算对，可能是因为题目没看清楚，题目的问题是given that the reimbursement is positive。根据key的提示，G(115)说明health care costs等于150，但是deductible是20，所以根据指数函数的无记忆性G(115)
=F(150)/(1-F(20))=F(150-20)=F(130)
第二题：
把等式右边根据方差和期望的定义展开，就可以得到右边=E(N^2) - (E(N))^2。其实这道题相当于给出了(N,λ) 的联合分布，让你求N的方差。

Thank you so much! this really helps me!