112. The article “Error Distribution in Navigation” (J. Institute of 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 f(x)
(.1)e.2⏐x⏐   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.