Refer to the U.S. Army Corps of Engineers' study of beach erosional hot spots, presented in Exercise 3.167 (p. 177). The data on the nearshore bar condition for six beach hot spots are reproduced in the accompanying table. Suppose you randomly select two of these six beaches and count x, the total number in the sample with a planar nearshore bar condition.
Beach Hot Spot...................................................Nearshore Bar Condition
Miami Beach, FL..................................................Single, shore parallel
Cone Island NY ................................................... Other
Surfside, CA ......................................................Single, shore parallel
Monmouth Beach, NJ.............................................Planar
Ocean City, NJ.....................................................Other
Spring Lake, NJ....................................................Planar
Based on Identification and Characterization of Erosional Hotspots, William & Mary Virginia Institute of Marine Science, U.S. Army Corps of Engineers Project Report, Mar.18, 2002.
a. List all possible pairs of beach hot spots that can be selected from the six.
b. Assign probabilities to the outcomes in part a.
c. For each outcome in part a, determine the value of x.
d. Form a probability distribution table for x.
e. Find the expected value of x. Interpret the result.