 1.1: A coin is tossed three times and the sequence of heads and tails is...
 1.2: Two sixsided dice are thrown sequentially, and the face values tha...
 1.3: An urn contains three red balls, two green balls, and one white bal...
 1.4: Draw Venn diagrams to illustrate De Morgans laws: (A B)c = Ac Bc (A...
 1.5: Let A and B be arbitrary events. Let C be the event that either A o...
 1.6: Verify the following extension of the addition rule (a) by an appro...
 1.7: Prove Bonferronis inequality: P(A B) P(A) + P(B) 1
 1.8: Prove that P __n i=1 Ai _ _n i=1 P(Ai )
 1.9: The weather forecaster says that the probability of rain on Saturda...
 1.10: Make up another example of Simpsons paradox by changing the numbers...
 1.11: The first three digits of a university telephone exchange are 452. ...
 1.12: In a game of poker, five players are each dealt 5 cards from a 52c...
 1.13: In a game of poker, what is the probability that a fivecard hand w...
 1.14: The four players in a bridge game are each dealt 13 cards. How many...
 1.15: How many different meals can be made from four kinds of meat, six v...
 1.16: How many different letter arrangements can be obtained from the let...
 1.17: In acceptance sampling, a purchaser samples 4 items from a lot of 1...
 1.18: Alot of n items contains k defectives, andm are selected randomly a...
 1.19: A committee consists of five Chicanos, two Asians, three African Am...
 1.20: A deck of 52 cards is shuffled thoroughly. What is the probability ...
 1.21: A fair coin is tossed five times. What is the probability of gettin...
 1.22: A standard deck of 52 cards is shuffled thoroughly, and n cards are...
 1.23: How many ways are there to place n indistinguishable balls in n urn...
 1.24: If n balls are distributed randomly into k urns, what is the probab...
 1.25: A woman getting dressed up for a night out is asked by her signific...
 1.26: The game of Mastermind starts in the following way: One player sele...
 1.27: If a fiveletterword is formed at random (meaning that all sequence...
 1.28: How many ways are there to encode the 26letter English alphabet in...
 1.29: Apoker player is dealt three spades and two hearts. He discards the...
 1.30: Agroup of 60 second graders is to be randomly assigned to two class...
 1.31: Six male and six female dancers perform the Virginia reel. This dan...
 1.32: A wine taster claims that she can distinguish four vintages of a pa...
 1.33: An elevator containing five people can stop at any of seven floors....
 1.34: Prove the following identity: _n k=0 _ n k _ m n n k = _ m n (Hint:...
 1.35: Prove the following two identities both algebraically and by interp...
 1.36: What is the coefficient of x3 y4 in the expansion of (x + y)7?
 1.37: What is the coefficient of x2 y2z3 in the expansion of (x + y + z)7?
 1.38: A child has six blocks, three of which are red and three of which a...
 1.39: A monkey at a typewriter types each of the 26 letters of the alphab...
 1.40: In how many ways can two octopi shake hands? (There are a number of...
 1.41: A drawer of socks contains seven black socks, eight blue socks, and...
 1.42: How many ways can 11 boys on a soccer team be grouped into 4 forwar...
 1.43: A software development company has three jobs to do. Two of the job...
 1.44: In how many ways can 12 people be divided into three groups of 4 fo...
 1.45: Show that if the conditional probabilities exist, then P(A1 A2 An) ...
 1.46: Urn A has three red balls and two white balls, and urn B has two re...
 1.47: Urn A has four red, three blue, and two green balls. Urn B has two ...
 1.48: An urn contains three red and two white balls. A ball is drawn, and...
 1.49: A fair coin is tossed three times. a. What is the probability of tw...
 1.50: Two dice are rolled, and the sum of the face values is six. What is...
 1.51: Answer again given that the sum is less than six.
 1.52: Suppose that 5 cards are dealt from a 52card deck and the first on...
 1.53: A fire insurance company has highrisk, mediumrisk, and lowrisk c...
 1.54: This problem introduces a simple meteorological model, more complic...
 1.55: This problem continues Example D of Section 1.5 and concerns occupa...
 1.56: A couple has two children. What is the probability that both are gi...
 1.57: There are three cabinets, A, B, and C, each of which has two drawer...
 1.58: A teacher tells three boys, Drew, Chris, and Jason, that two of the...
 1.59: A box has three coins. One has two heads, one has two tails, and th...
 1.60: A factory runs three shifts. In a given day, 1% of the items produc...
 1.61: Suppose that chips for an integrated circuit are tested and that th...
 1.62: Show that if P(A  E) P(B  E) and P(A  Ec) P(B  Ec), then P(A) P...
 1.63: Suppose that the probability of living to be older than 70 is .6 an...
 1.64: If B is an event, with P(B) > 0, show that the set function Q(A) = ...
 1.65: Show that if A and B are independent, then A and Bc as well as Ac a...
 1.66: Show that is independent of A for any A.
 1.67: Show that if A and B are independent, then P(A B) = P(A) + P(B) P(A...
 1.68: If A is independent of B and B is independent of C, then A is indep...
 1.69: If A and B are disjoint, can they be independent?
 1.70: If A B, can A and B be independent?
 1.71: Show that if A, B, and C are mutually independent, then A B and C a...
 1.72: Suppose that n components are connected in series. For each unit, t...
 1.73: A system has n independent units, each of which fails with probabil...
 1.74: What is the probability that the following system works if each uni...
 1.75: This problem deals with an elementary aspect of a simple branching ...
 1.76: Here is a simple model of a queue. The queue runs in discrete time ...
 1.77: A player throws darts at a target. On each trial, independently of ...
 1.78: This problem introduces some aspects of a simple genetic model. Ass...
 1.79: Many human diseases are genetically transmitted (for example, hemop...
 1.80: If a parent has genotype Aa, he transmits either A or a to an offsp...
Solutions for Chapter 1: Probability
Full solutions for Mathematical Statistics and Data Analysis  3rd Edition
ISBN: 9788131519547
Solutions for Chapter 1: Probability
Get Full SolutionsThis textbook survival guide was created for the textbook: Mathematical Statistics and Data Analysis, edition: 3. Mathematical Statistics and Data Analysis was written by and is associated to the ISBN: 9788131519547. Chapter 1: Probability includes 80 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 80 problems in chapter 1: Probability have been answered, more than 22160 students have viewed full stepbystep solutions from this chapter.

2 k factorial experiment.
A full factorial experiment with k factors and all factors tested at only two levels (settings) each.

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

All possible (subsets) regressions
A method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions

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

Central tendency
The tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.

Conditional mean
The mean of the conditional probability distribution of a random variable.

Conditional probability
The probability of an event given that the random experiment produces an outcome in another event.

Contingency table.
A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria

Continuous distribution
A probability distribution for a continuous random variable.

Control limits
See Control chart.

Convolution
A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.

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 .

Defectsperunit control chart
See U chart

Deming’s 14 points.
A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality

Distribution function
Another name for a cumulative distribution function.

Empirical model
A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.

Error sum of squares
In analysis of variance, this is the portion of total variability that is due to the random component in the data. It is usually based on replication of observations at certain treatment combinations in the experiment. It is sometimes called the residual sum of squares, although this is really a better term to use only when the sum of squares is based on the remnants of a modelitting process and not on replication.

Experiment
A series of tests in which changes are made to the system under study

Gaussian distribution
Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications

Hat matrix.
In multiple regression, the matrix H XXX X = ( ) ? ? 1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .