141. The article “Error Distribution in Navigation”

(J. Institut. Navigation, 1971: 429– 442) 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

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.