An electronic device consists of two components. Let X and Y be the length of ti

Question

An electronic device consists of two components. Let X and Y be the length of time until failure (in years) of the first and second component, respectively. Assume that (X,Y) has the probability density function f(x,y)=k(xy^2+2x^2y) if 0<=x<=6 and 0<=y<=8 and 0 otherwise. Find the expected lifetimes of the two components. What is the probability that the device will last longer than three years? What is the covariance of the component lifetimes of the device?

Explanation / Answer

For X~N(28, 5^2) a) No refund if it is ok for at least 24 months, P{X>24} = P{Z>z}, where z = (24-28)/5 = 4/5 = - 0.80. P{Z> -0.80} = 1 - P{Z< -0.80} = 1 - 0.2119. Or, % replaced, P{Z< -0.80} = 0.2119, 21%. b) Now, you want P{Z

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