3044sample2s09 - 1 ISyE 3044 Old Questions from Exam#2 1...

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1 ISyE 3044 — Old Questions from Exam #2 1. Consider the following 10 pseudo-random numbers (read from left to right): 0.98 0.51 0.66 0.97 0.31 0.08 0.27 0.42 0.16 0.68 (a) Use the first two numbers to generate two observations from the N (0 , 1) distribution. (b) Use the observations from part (a) to generate two observations from the normal distribution with mean 1 and variance 4. (c) Use all 10 numbers to generate an observation from the N (0 , 1) distribution. (d) Use as many numbers as you need to generate an observation from the Poisson( λ = 1) distribution. (e) Use as many numbers as you need to generate an observation from the geometric( p = 0 . 9) distribution. 2. The random variable X has density function f ( x ) = | x | , - 1 x 1. (a) Find the mean of X . (b) Apply the inverse-transform method to derive formula(s) for generating realizations of X . (c) Use the random number 0.75 to generate a realization of X . 3. The scope of a simulation project was the estimation of the mean time, say μ , it takes to produce an item. We used 10 independent runs and the central limit theorem to compute the following 95% confidence interval for μ : (4 . 8 , 12 . 4). (a) What is the estimate of μ ? (b) What is the relative error of this estimate? (c) Is the following statement correct? Yes No “The interval (4 . 8 , 12 . 4) contains the true mean with probability 0.95.” (d) Compute a 90% confidence interval for μ . 4. Consider the following 20 random numbers (read from left to right, and then down).
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