Experiments, Random Variables, and Distributions
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10. The following examples are experiments and their associated random variables. In each case identify the values the random variable can assume and state whether the random variable is discrete or continuous.
a. Take a 20-question exam
Number of questions answered correctly
b. Observe cars arriving at a tollbooth for I hour
Number of cars arriving at the tollbooth
c. Audit SO tax returns
Number of returns containing errors
d. Observe an employee's work for 8 hours
Number of nonproductive hours
e. Weigh a shipment of goods
Number of pounds
11. Suppose a manager must choose between the following two mathematical models of a given situation: (a) a relatively simple model that is a reasonable approximation of the real situation and (b) a thorough and complex model that is the most accurate mathematical representation of the real situation. Why might the model described in (a) be preferred by the manager?
12. A sample of 100 customers of Washington Gas resulted in the following frequency distribution of monthly charges:
Amount Number
0-49 13
50-99 22
100-149 34
150-199 26
200-249 5
a Let A be the event that monthly charges are $150 or more. Find P(A).
b. Let B be the event that monthly charges are less than $150. Find P(B).
13. Suppose that a sample space has five equally likely experimental outcomes: E1, B2, E3, E4, and E5. Let
A = {E1, E2}
B = {E3, E$}
C = {E, E3, E5}
a. Find P(A), P(B). and P(C)
b. P(A U B). Are A and B mutually exclusive?
c. Find Ac. Ct
d. EindAUBCandP(AUBC)
e. Find P(B U C)
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Solution Summary
This problem set has four questions involving random variables, mathematical models, probabilities of events, and probability rules (union, intersection, complement).
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Probability
10. The following examples are experiments and their associated random variables. In each case identify the values the random variable can assume and state whether the random variable is discrete or continuous.
a. Take a 20-question exam
Number of questions answered correctly
Possible values: 0, 1, 2, ... , 19, 20
discrete
b. Observe cars arriving at a tollbooth for 1 hour
Number of cars arriving at the tollbooth
Possible values: 0, 1, 2, ... up to the maximum (for example, if the tollbooth can handle 1 car per minute, the maximum number of cars is 60)
discrete
c. Audit SO tax returns
Number of returns containing errors
Possible values: 0, 1, 2, ... up to the number of returns you audit
discrete
d. Observe an ...
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