MATH 3170 Study Guide - Midterm Guide: Poisson Point Process, Exponential Distribution, Random Variable
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Instruction: the actual exam will be similar to the practice test (possibly with less questions in each problem, or slightly di erent format). The total will be 70 points in total, 10 points for conceptional questions, 30 points (2-3 problems) for poisson processes, and 30 points (2-3 problems) for renewal processes. Calculator will be allowed though you are not required to write down your answers in decimals. You must include all work to receive full credit! Conceptional (1) xi exp( i), 1 i n, are iid. What is the distribution of x = min{x1, , xn}? (2) yi pois( i), 1 i n, are iid. What is the distribution of y = y1 + + yn? (3) write down two di erent de nitions of a poisson process n (t) with a rate . (4) write down the de nition of a renewal process. Solution (1) x exp( 1 + + n).
