 1.4.1: Gottfried Wilhelm Leibniz (16461716), the German mathematician, phi...
 1.4.2: Suppose that 33% of the people have O+ blood and 7% have O. What is...
 1.4.3: The probability that an earthquake will damage a certain structure ...
 1.4.4: Suppose that the probability that a driver is a male, and has at le...
 1.4.5: Suppose that 75% of all investors invest in traditional annuities a...
 1.4.6: In a horse race, the odds in favor of the first horse winning in an...
 1.4.7: Excerpt from the TV show The Rockford Files: Rockford: There are on...
 1.4.8: A company has only one position with three highly qualified applica...
 1.4.9: In a psychiatric hospital, the number of patients with schizophreni...
 1.4.10: Let A and B be two events. Prove that P (AB) P (A) + P (B) 1.
 1.4.11: A card is drawn at random from an ordinary deck of 52 cards. What i...
 1.4.12: Which of the following statements is true? If a statement is true, ...
 1.4.13: Suppose that in the Baltimore metropolitan area 25% of the crimes o...
 1.4.14: Let A, B, and C be three events. Prove that P (A B C) = P (A) + P (...
 1.4.15: Let A, B, and C be three events. Show that exactly two of these eve...
 1.4.16: Eleven chairs are numbered 1 through 11. Four girls and seven boys ...
 1.4.17: A ball is thrown at a square that is divided into n2 identical squa...
 1.4.18: Among 33 students in a class, 17 of them earned As on the midterm e...
 1.4.19: From a small town 120 persons were selected at random and asked the...
 1.4.20: The coefficients of the quadratic equation x2 + bx + c = 0 are dete...
 1.4.21: Two integers m and n are called relatively prime if 1 is their only...
 1.4.22: A number is selected randomly from the set {1, 2, . . . , 1000}. Wh...
 1.4.23: The secretary of a college has calculated that from the students wh...
 1.4.24: From an ordinary deck of 52 cards, we draw cards at random and with...
 1.4.25: A number is selected at random from the set of natural numbers {1, ...
 1.4.26: For a Democratic candidate to win an election, she must win distric...
 1.4.27: Two numbers are successively selected at random and with replacemen...
 1.4.28: Let A1, A2, A3, ... be a sequence of events of a sample space. Prov...
 1.4.29: Let A1, A2, A3,... be a sequence of events of an experiment. Prove ...
 1.4.30: In a certain country, the probability is 49/50 that a randomly sele...
 1.4.31: Let P be a probability defined on a sample space S. For events A of...
 1.4.32: (The Hat Problem) A game begins with a team of three players enteri...
Solutions for Chapter 1.4: Basic Theorems
Full solutions for Fundamentals of Probability, with Stochastic Processes  3rd Edition
ISBN: 9780131453401
Solutions for Chapter 1.4: Basic Theorems
Get Full SolutionsSince 32 problems in chapter 1.4: Basic Theorems have been answered, more than 15010 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Fundamentals of Probability, with Stochastic Processes was written by and is associated to the ISBN: 9780131453401. Chapter 1.4: Basic Theorems includes 32 full stepbystep solutions. This textbook survival guide was created for the textbook: Fundamentals of Probability, with Stochastic Processes, edition: 3.

Acceptance region
In hypothesis testing, a region in the sample space of the test statistic such that if the test statistic falls within it, the null hypothesis cannot be rejected. This terminology is used because rejection of H0 is always a strong conclusion and acceptance of H0 is generally a weak conclusion

Analytic study
A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study

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.

Backward elimination
A method of variable selection in regression that begins with all of the candidate regressor variables in the model and eliminates the insigniicant regressors one at a time until only signiicant regressors remain

Bayesâ€™ theorem
An equation for a conditional probability such as PA B (  ) in terms of the reverse conditional probability PB A (  ).

Bias
An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.

Categorical data
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.

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

Combination.
A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.

Control limits
See Control chart.

Covariance
A measure of association between two random variables obtained as the expected value of the product of the two random variables around their means; that is, Cov(X Y, ) [( )( )] =? ? E X Y ? ? X Y .

Critical region
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.

Crossed factors
Another name for factors that are arranged in a factorial experiment.

Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.

Density function
Another name for a probability density function

Discrete random variable
A random variable with a inite (or countably ininite) range.

Error of estimation
The difference between an estimated value and the true value.

F distribution.
The distribution of the random variable deined as the ratio of two independent chisquare random variables, each divided by its number of degrees of freedom.

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

Fraction defective control chart
See P chart