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Chapter 5: Q 5.8. (page 216)
Suppose that C and D are mutually exclusive events such that and Determine .
As a result, has a value of
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Major Hurricanes. The Atlantic Hurricane Database extends back to 1851, recording among other things the number of major hurricanes striking the U.S. Atlantic and Gulf Coast per year. A major hurricane is a hurricane measuring at least a Category 3 on the Saffir-Simpson hurricane wind scale (i.e., with winds of at least 110 mph). As published by the National Oceanic & Atmospheric Administration and the Atlantic Oceanographic & Meteorological Laboratory, the following table provides a probability distribution for the number of major hurricanes, Y, for a randomly selected year between 1851 and 2012.
Use random-variable notation to represent each of the following events. The year had
a. at least one major hurricane.
b. exactly three major hurricanes.
c. between 2 and 4 major hurricanes, inclusive.
Use the special addition rule and the probability distribution to determine
d. P(Y 鈮� 1).
e. P(Y = 3).
f. P(2 鈮� Y鈮� 4)
An experiment has 40 possible outcomes, all equally likely. An event can occur in 25 ways. The probability that the event is .
Expected Utility. One method for deciding among various investment involves the concept of expected utility. Economists describe the importance of various levels of wealth by using utility functions. For instance, in most case, a single dollar is more important (has greater utility ) for someone with little wealth than for someone with greater wealth Consider two investments, say investment A and B. Measured in thousand of dollars, suppose that investment A yields 0, 1, and 4 with probability 0.1 and16 with probability 0.5, 0.3 and 0.2 respectively. Let Y denote the yield of an investment. For the two investment, determine and compare.
Part (a) The mean of Y, the expected yield.
Part (b) The mean of ,the expected utility, using the utility function role="math" localid="1651845051902" Interpret the utility function
Part (c) The mean of ,the expected utility, using the utility function . Interpret the utility function v
Space Shuttles. The National Aeronautics and Space Administration (NASA) compiles data on space-shuttle launches and publishes them on its website. The following table displays a frequency distribution for the number of crew members on each shuttle mission from April 12, 1981 to July 8, 2011.
| Crew Size | 2 | 4 | 5 | 6 | 7 | 8 |
| Frequency | 4 | 3 | 36 | 28 | 63 | 1 |
Let X denote the crew size of a randomly selected shuttle mission between the aforementioned dates.
a. What are the possible values of the random variable X?
b. Use random-variable notation to represent the event that the shuttle mission obtained has a crew size of 7.
c. Find P(X = 4); interpret in terms of percentages.
d. Obtain the probability distribution of X.
e. Construct a probability histogram for X.
Suppose that a simple random sample is taken from a finite population in which each member is classified as either having or not having a specified attribute. Fill in the following blanks.
(a) If sampling is with replacement, the probability distribution of the number of members sampled that have the specified attribute is a distribution.
(b) If sampling is without replacement, the probability distribution of the number of members sampled that have the specified attribute is a distribution.
(c) If sampling is without replacement and the sample size does not exceed % of the population size, the probability distribution of the number of members sampled that have the specified attribute can be approximated by a distribution.
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