 2.2.1: How many sixdigit numbers are there? How many of them contain the ...
 2.2.2: How many different fiveletter codes can be made using a, b, c, d, ...
 2.2.3: The population of a town is 20,000. If each resident has three init...
 2.2.4: In how many different ways can 15 offices be painted with four diff...
 2.2.5: In flipping a fair coin 23 times, what is the probability of all he...
 2.2.6: In how many ways can we draw five cards from an ordinary deck of 52...
 2.2.7: Two fair dice are thrown. What is the probability that the outcome ...
 2.2.8: Mr. Smith has 12 shirts, eight pairs of slacks, eight ties, and fou...
 2.2.9: A multiplechoice test has 15 questions, each having four possible ...
 2.2.10: Suppose that in a state, license plates have three letters followed...
 2.2.11: A library has 800,000 books, and the librarian wants to encode each...
 2.2.12: How many n m arrays (matrices) with entries 0 or 1 are there?
 2.2.13: How many divisors does 55,125 have? Hint: 55,125 = 325372.
 2.2.14: A delicatessen has advertised that it offers over 500 varieties of ...
 2.2.15: How many fourdigit numbers can be formed by using only the digits ...
 2.2.16: In a mental health clinic there are 12 patients. A therapist invite...
 2.2.17: Suppose that four cards are drawn successively from an ordinary dec...
 2.2.18: A campus telephone extension has four digits. How many different ex...
 2.2.19: There are N types of drugs sold to reduce acid indigestion. A rando...
 2.2.20: Jenny, a probability student, having seen Example 2.6 and its solut...
 2.2.21: A salesperson covers islands A, B, ... , I . These islands are conn...
 2.2.22: In a large town, Kennedy Avenue is a long northsouth avenue with m...
 2.2.23: An integer is selected at random from the set {1, 2, . . . , 1, 000...
 2.2.24: How many divisors does a natural number N have? Hint: A natural num...
 2.2.25: In tossing four fair dice, what is the probability of tossing, at m...
 2.2.26: A delicatessen advertises that it offers over 3000 varieties of san...
 2.2.27: One of the five elevators in a building leaves the basement with ei...
 2.2.28: The elevator of a fourfloor building leaves the first floor with s...
 2.2.29: A number is selected randomly from the set {0000, 0001, 0002, . . ....
 2.2.30: What is the probability that a random rdigit number (r 3) contains...
Solutions for Chapter 2.2: Counting Principle
Full solutions for Fundamentals of Probability, with Stochastic Processes  3rd Edition
ISBN: 9780131453401
Solutions for Chapter 2.2: Counting Principle
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 2.2: Counting Principle includes 30 full stepbystep solutions. Since 30 problems in chapter 2.2: Counting Principle have been answered, more than 13978 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Fundamentals of Probability, with Stochastic Processes, edition: 3. Fundamentals of Probability, with Stochastic Processes was written by and is associated to the ISBN: 9780131453401.

aerror (or arisk)
In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).

Arithmetic mean
The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average

Asymptotic relative eficiency (ARE)
Used to compare hypothesis tests. The ARE of one test relative to another is the limiting ratio of the sample sizes necessary to obtain identical error probabilities for the two procedures.

Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability

Bernoulli trials
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.

Bivariate distribution
The joint probability distribution of two random variables.

Causal variable
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable

Causeandeffect diagram
A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.

Chisquare (or chisquared) random variable
A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.

Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.

Conidence coeficient
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.

Continuity correction.
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.

Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.

Cumulative normal distribution function
The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.

Cumulative sum control chart (CUSUM)
A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t

Density function
Another name for a probability density function

Distribution function
Another name for a cumulative distribution function.

Expected value
The expected value of a random variable X is its longterm average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.

Fraction defective
In statistical quality control, that portion of a number of units or the output of a process that is defective.

Geometric mean.
The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .