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Chapter 5: Q.7 (page 346)
What is the area under f(x) if the function is a continuous probability density function?
The area under will be if the function is continuous probability density function
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A continuous probability function is restricted to the portion between x = 0 and 7. What is P(x = 10)?
Suppose that the length of long distance phone calls, measured in minutes, is known to have an exponential distribution with the average length of a call equal to eight minutes.
a. Define the random variable.
b. Is X continuous or discrete?
c.
d.
e.
f. Draw a graph of the probability distribution. Label the axes.
g. Find the probability that a phone call lasts less than nine minutes.
h. Find the probability that a phone call lasts more than nine minutes.
i. Find the probability that a phone call lasts between seven and nine minutes.
j. If 25 phone calls are made one after another, on average, what would you expect the total to be? Why?
The time (in years) after reaching age that it takes an individual to retire is approximately exponentially distributed with a mean of about five years. Suppose we randomly pick one retired individual. We are interested in the time after age
to retirement.
a. Define the random variable.
b. Is continuous or discrete?
c.
d.
e.
f. Draw a graph of the probability distribution. Label the axes.
g. Find the probability that the person retired after age .
h. Do more people retire before age or after age ?
i. In a room of people over age , how many do you expect will NOT have retired yet?
Use the following information to answer the next eight exercises. A distribution is given as .
What isa? What does it represent?
Use the following information to answer the next ten exercises. A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be modeled by the following distribution:
What type of distribution is this?
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