The article "Error Distribution in Navigation" (J. of the 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 5 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.