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stormhold
March 24th 2009, 10:32 PM
The time, T, that a manufacturing system is out of operation has cumulative distribution function.
F(t) = 1 − (2/t)^2
for t > 2,
0 otherwise.

The resulting cost to the company is Y = T2. Determine the density function of Y , for y > 4.

NoMoreExams
March 24th 2009, 11:34 PM
I assume you mean Y = T^2, show some work this seems pretty straightforward.

stormhold
March 25th 2009, 08:31 AM
I first get f(t)=F'(t)=8t^-3, then f(y)=F(t^1/2)=(1/2)t^(-1/2)f(t^1/2)=4t^(-2). but the answer said it is 4y^(-2).

So can you explain to me.

calculusdork
March 25th 2009, 08:34 AM
http://www.actuary.com/actuarial-discussion-forum/showthread.php?t=9903&highlight=resulting+cost+company

Answer in a previous thread.

stormhold
March 25th 2009, 11:27 AM
I got it now. I kinda blurred between t and y. Thanks.