The article Error Distribution in Navigation (J. Institute

Chapter 4, Problem 4.120

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The article Error Distribution in Navigation (J. Institute of Navigation, 1971: 429442) suggests that the frequency distribution of positive errors (magnitudes of errors) is well approximated by an exponential distribution. Let X the lateral position error (nautical miles), which can be either negative or positive. Suppose the pdf of X is f(x) (.1)e .2x x a. Sketch a graph of f(x) and verify that f(x) is a legitimate pdf (show that it integrates to 1). b. Obtain the cdf of X and sketch it. c. Compute P(X 0), P(X 2), P( 1 X 2), and the probability that an error of more than 2 miles is made.

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