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# 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

Solutions for Chapter 2.2
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##### ISBN: 9780131453401

This expansive textbook survival guide covers the following chapters and their solutions. Chapter 2.2: Counting Principle includes 30 full step-by-step solutions. Since 30 problems in chapter 2.2: Counting Principle have been answered, more than 13978 students have viewed full step-by-step 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.

Key Statistics Terms and definitions covered in this textbook
• a-error (or a-risk)

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

• Cause-and-effect diagram

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

• Chi-square (or chi-squared) 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 long-term 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 .

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