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# Discrete probability distribution problems

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11. A technician services mailing machines at companies in the Phoenix area. Depending on the type of malfunction, the service call can take 1,2, 3, or 4 hours. The different types of malfunction occur at about the same frequency.

A. Develop a probability distribution for the duration of a service call.
B. Draw a graph of the probability distribution.
C. Show that your probability distribution satisfies the conditions required for a discrete probability function.
D. What is the probability a service call will take 3 hours?
E. A service call has just come in, but the type of malfunction is unknown. It is 3:00 PM and service technicians usually get off at 5:00 P.M. What is the probability the service technician will have to work overtime to fix the machine today?

13. A psychologist determined that the number of sessions required to obtain the trust of a new patients is either 1, 2, or 3. Let x be random variable indicating the number of sessions required to gain the patient's trust. The following probability function has been proposed.

F(x) = for x = 1, 2, or 3
A. is this probability function valid? Explain
B. what is the probability that it takes exactly 2 sessions to gain the patient's trust?
C. What is the probability that it takes at least 2 sessions to gain the patient's trust?

15. The following table provides a probability distribution for the random variable x.

x f(x)

3 .25
6 .50
9 .25
A. Compute E(x), the expected value of x.

2
B. Compute , the variance of x.
C. compute , the standard deviation of x.

17. A volunteer ambulance service handles 0 to 5 service calls on any given day. The probability distribution for the number of service calls is as follows.

Number of service calls probability number of service calls probability
0 .10 3 .20
1 .15 4 .15
2 .30 5 .10
a. what is the expected number of service calls?
b. What is the variance in the number of service calls? What is the standard deviation?

See attached file for full problem description.