A life insurance company classifies its customers as being either high risk or low risk. If 20% of the customers are high risk, and high risk customers are three times more likely to file a claim, hat percentage of claims that are filed come from high risk customers?

Question

A life insurance company classifies its customers as being either high risk or low risk.  If 20% of the customers are high risk, and high risk customers are three times more likely to file a claim, hat percentage of claims that are filed come from high risk customers?

anonymous · Answer

H + L = 100% customers

H = 20%, L = 80%

3 H + L = claims

(3)(20) + (1)(80) = claims

60 + 80  = 140

60/140 due to H and 80/140 due to L

make fractions into % for answer.

anonymous · Answer

Thanks - I knew this was an easy problem, but I just wasn't sure where to start.

anonymous · Answer

Okay, I have another one here:

Suppose that $$X _{1},...,X _{100} $$ are random variables with $$E(X _{i})=100, E(X _{i}^{2})=10100$$  

If $$Cov(X _{i},X _{j})=-1, i \neq j$$ what is Var(S), where$$S=\sum_{i=1}^{100}X _{i}$$?

I got Var(S) to be 100, which is the correct answer but what good does knowing the covariance do?  I tried using it, and it just throws everything off.