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Short-Term Actuarial Math Old Exam C Forum

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  #1  
Old 01-19-2015, 11:47 PM
mac805 mac805 is offline
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I am getting the correct E[S] and Var(S):

E[S] = lamda * theta
Var(S) = 2 * lamda * theta^2

However, I don't understand why v = 4 and a = 3. I am getting v = 2 and a = 1, which is apparently a trap.

I am getting:

v = E[2 * lamda * theta^2] = 2*1*1 = 2
a = Var(lamda * theta) = 1*1 = 1

Help please!
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Old 01-20-2015, 12:01 AM
Academic Actuary Academic Actuary is offline
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What are the distributions for lambda and theta? One mistake is the variance of a product isn't the product of variances even if the RVs are independent.
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Old 01-20-2015, 09:51 AM
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sicn@rf sicn@rf is offline
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Quote:
Originally Posted by mac805 View Post
I am getting the correct E[S] and Var(S):

E[S] = lamda * theta
Var(S) = 2 * lamda * theta^2

However, I don't understand why v = 4 and a = 3. I am getting v = 2 and a = 1, which is apparently a trap.

I am getting:

v = E[2 * lamda * theta^2] = 2*1*1 = 2
a = Var(lamda * theta) = 1*1 = 1

Help please!
You are on the right track..
remember
1. E[theta^2]=2 since theta is Possion, Var[theta]+E[theta]^2 = 1 + 1^2
therefore E[2 * lamda * theta^2] = 2 * 1 * 2 = 4
2. Var[lambda *theta]=E [lamba^2]*E[theta^2] - E[theta]^2 * E[lambda]^2 = 2*2 -1*1
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  #4  
Old 01-20-2015, 12:20 PM
mac805 mac805 is offline
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Thank you!
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