Actuarial Outpost SOA #181
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 Short-Term Actuarial Math Old Exam C Forum

#1
01-19-2015, 10:47 PM
 mac805 Member SOA Join Date: Dec 2008 Location: Pleasant Hill, CA Studying for Group Health Advanced College: Cal Poly, San Luis Obispo Alumni Favorite beer: Yes Posts: 79
SOA #181

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

#2
01-19-2015, 11:01 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,475

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.
#3
01-20-2015, 08:51 AM
 sicn@rf Member SOA Join Date: Nov 2008 Posts: 175

Quote:
 Originally Posted by mac805 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
01-20-2015, 11:20 AM
 mac805 Member SOA Join Date: Dec 2008 Location: Pleasant Hill, CA Studying for Group Health Advanced College: Cal Poly, San Luis Obispo Alumni Favorite beer: Yes Posts: 79

Thank you!