identify a problem in an IT-related system where statistical methods could be used to analyze, evaluate, and recommend performance improvements for the system.

Summarize the problem, and discuss how you would use the discrete mathematics, probability, and statistical methods from this course to analyze the associated data, present the information, and draw inferences to develop a solution that would improve system performance. Explain your reasoning.

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Fourier analysis 1. Say, X1 (t) = A( 2 . t/9) x e-15 .t/71 x cos (2 n . t - Tt/) ; It| $ 5 , and zero elsewhere. Using the format of time - frequency pairs: a. Produce an educated guess (by hand) for the spectral decomposition of the signal X, (t) b. Carry on the spectral decomposition computation of X, (t) c. Compare the results in parts a and b above. d. Consider this time contamination with additive white Gaussian noise.

Dj cannot be 9) In the multiple regression model, the adjusted Ra A) cannot be negative. B) will never be greater than the regression R?. C) equals the square of the correlation coefficient r. D) cannot decrease when an additional explanatory variable is added. 10) A statistical analysis is internally valid if A) its inferences and conclusions can be generalized from the population and setting studied to other populations and settings. B) statistical inference is conducted inside the sample period. C) the hypothesized parameter value is inside the confidence interval. D) the statistical inferences about causal effects are valid for the population being studied.

In a single channel automatic car wash, cars arrive following Poisson distribution at the rate of 20 per hour. It takes an average of 2 minutes to wash a car, and the service time follows exponential distribution. Find the following operating characteristics of the system (10 marks). a) What is the probability that 4 cars arrive within 10 minutes? b) What is the probability that no car arrives within 5 minutes? c) What is the probability that a car is washed in less than 1.5 minutes.

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