STATISTC 515 Midterm: STATS 515 UMass Amherst S515.Spring17.Midterm2
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Instruction: notes, calculators, and other electronics are not allowed, show all your work. You need to fully justify all of your answers. A correct answer with insu cient justi cation may receive no credit: a formula sheet is provided in the last page, you have 2 hours to complete the exam. 2: answer each of these questions with complete justi cation. (a) (5 point) suppose y is uniformly distributed over the interval [0, 2]. Compute e(3y 3). (b) (4 points) suppose y is normally distributed with mean 1 and variance 2. 0 x 1 otherwise g(x) =( 1. 1 x 2 if otherwise: the lifetime of a certain electric machine is modeled by an exponential distribution with mean years. You can leave your nal answer in terms of logarithms. 3 (b) (8 points) now assume that the mean of y is 5 (that is, = 5).
