prob.part37.75_76 - 2.2. CONTINUOUS DENSITY FUNCTIONS 67...

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2.2. CONTINUOUS DENSITY FUNCTIONS 67 1 - z 1 - z 1 - z 1 - z E Figure 2.19: Calculation of F Z . 20 40 60 80 100 120 0.005 0.01 0.015 0.02 0.025 0.03 f (t) = (1/30) e - (1/30) t Figure 2.20: Exponential density with λ = 1 / 30.
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68 CHAPTER 2. CONTINUOUS PROBABILITY DENSITIES 0 20 40 60 80 100 0 0.005 0.01 0.015 0.02 0.025 0.03 Figure 2.21: Residual lifespan of a hard drive. is distributed according to the exponential density. We will assume that this model applies here, with λ = 1 / 30. Now suppose that we have been operating our computer for 15 months. We assume that the original hard drive is still running. We ask how long we should expect the hard drive to continue to run. One could reasonably expect that the hard drive will run, on the average, another 15 months. (One might also guess that it will run more than 15 months, since the fact that it has already run for 15 months implies that we don’t have a lemon.) The time which we have to wait is a new random variable, which we will call Y . Obviously, Y = X - 15. We can write a computer program to produce a sequence of simulated Y -values. To do this, we ±rst produce a sequence of X ’s, and discard those values which are less than
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prob.part37.75_76 - 2.2. CONTINUOUS DENSITY FUNCTIONS 67...

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