STAT 400 Midterm: STAT400 COHEN-J SPRING2012 0101 MID EXAM

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Midterm 2a: suppose x and y are random variables de ned on the same sample space with the following joint probability mass function. Assume the lifetime of each component is exponentially distributed with pa- rameter and that the components function independently. Find the cumulative density function for the system lifetime. More precisely , if x is the random variable de ned by (x = t) means the system dies at time t nd. 0, otherwise and fy (y) =( 1, 0 y 1. 0, otherwise. (a) find the joint probability density function fx,y (x, y) of x and y . (hint: since x and y are independent fx,y (x, y) is the product of fx (x) and fy (y). This product is not so easy to compute, the point is to gure out where it is zero and where it is one in the plane.