Standard Probability Distributions - Advanced Probability Theory for Biomedical Engineers - page 38

4. Determine E ( x 2 ).

10. Let random variable x be Bernoulli with n = 15 and p = 0 .

2

11. Suppose x is a Bernoulli random variable with η = 10 and σ = 10 / 3. Determine:

(a) q, (b) n, (c) p.
12. An electronics manufacturer is evaluating its quality control program. The current
procedure is to take a sample of 5 from 1000 and pass the shipment if not more than 1
component is found defective. What proportion of 20% defective components will be
shipped?
13. Repeat Problem 1, when appropriate, using the Poisson approximation to the Bernoulli
PMF.
14. A certain intersection averages 3 traffic accidents per week. What is the probability that
more than 2 accidents will occur during any given week?
15. Suppose that on the average, a student makes 6 mistakes per test. Determine the
probability that the student makes: (a) at least 1 mistake; (b) from 3 to 5 mistakes;
(c) exactly 2 mistakes; (d) more than the expected number of mistakes.
16. On the average, Professor Rensselaer gives 11 quizzes per quarter in Introduction to
Random Processes. Determine the probability that: (a) from 8 to 12 quizzes are given
during the quarter; (b) exactly 11 quizzes are given during the quarter; (c) at least 10
quizzes are given during the quarter; (d) at most 9 quizzes are given during the quarter.
17. Suppose a typist makes an average of 30 mistakes per page. (a) If you give him a one
page letter to type, what is the probability that he makes exactly 30 mistakes? (b) The
typist decides to take typing lessons, and, after the lessons, he averages 5 mistakes per
page. You give him another one page letter to type. What is the probability of him
making fewer than 5 mistakes. (c) With the 5 mistakes per page average, what is the
probability of him making fewer than 50 mistakes in a 25 page report?
18. On the average, a sample of radioactive material emits 20 alpha particles per minute.
What is the probability of 10 alpha particles being emitted in: (a) 1 min, (b) 10 min?
(c) Many years later, the material averages 6 alpha particles emitted per minute. What
is the probability of at least 6 alpha particles being emitted in 1 min?
19. At Fargo Polytechnic Institute (FPI), a student may take a course as many times as
desired. Suppose the average number of times a student takes Introduction to Random
Processes is 1.5. (Professor Rensselaer, the course instructor, thinks so many students
repeat the course because they enjoy it so much.) (a) Determine the probability that a
student takes the course more than once. (b) The academic vice-president of FPI wants
to ensure that on the average, 80% of the students take the course at most one time. To
what value should the mean be adjusted to ensure this?