Beach erosional hot spots. Refer to the U.S. Army Corps of Engineers’ study of beach erosional hot spots, presented in Exercise 3.173 (p. 171). The data on the near shore 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 near shore bar condition.
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.
Exercise 3.173
Beach erosional hot spots. Beaches that exhibit high erosion rates relative to the surrounding beach are defined as erosional hot spots . The U.S. Army Corps of Engineers is conducting a study of beach hot spots. Through an online questionnaire, data are collected on six beach hot spots. The data are listed in the next table.
a. Suppose you record the near shore bar condition of each beach hot spot. Give the sample space for this experiment.
b. Find the probabilities of the sample points in the sample space you defined in part a.
c. What is the probability that a beach hot spot has either a planar or single, shore-parallel near shore bar condition?
d. Now suppose you record the beach condition of each beach hot spot. Give the sample space for this experiment.
e. Find the probabilities of the sample points in the sample space you defined in part d.
f. What is the probability that the condition of the beach at a particular beach hot spot is not flat?