An insurance company sells two types of auto insurance policies: Basic and Deluxe. The time until the next Basic Policy claim is an exponential random variable with mean 6 days. The time until the next Deluxe Policy claim is an independent exponential random variable with mean 7 days. What is the probability that the next claim will be a Deluxe Policy claim?
a) 0.462
b) 0.562
c) 0.362
d) 0.529
e) 0.329
I know how to do this but I can't get the double integral to work out...
As I understand it:
x - time until Basic claim
y - time until Deluxe claim
Find P(y < x)
since the two functions are independent, we have:
f_XY(x,y) = f_X(x) * f_Y(y) = (1/6)e^(-x/6) * (1/7)e^(-y/7)
then you would just double integrate f(x,y) from
int(0 to infinity) int(0 to x) of f_XY(x,y) dydx
I don't know why I am having such a hard time integrating this... I came up with the answer .4487...
Is there a trick to solving this other than just brute force. Any chance you can use the Survival function? :embarrassed:
a) 0.462
b) 0.562
c) 0.362
d) 0.529
e) 0.329
I know how to do this but I can't get the double integral to work out...
As I understand it:
x - time until Basic claim
y - time until Deluxe claim
Find P(y < x)
since the two functions are independent, we have:
f_XY(x,y) = f_X(x) * f_Y(y) = (1/6)e^(-x/6) * (1/7)e^(-y/7)
then you would just double integrate f(x,y) from
int(0 to infinity) int(0 to x) of f_XY(x,y) dydx
I don't know why I am having such a hard time integrating this... I came up with the answer .4487...
Is there a trick to solving this other than just brute force. Any chance you can use the Survival function? :embarrassed:
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