 7.7.1: A player throws a fair die and simultaneouslyflips a fair coin. If ...
 7.7.2: The game of Clue involves 6 suspects, 6 weapons,and 9 rooms. One of...
 7.7.3: Gambles are independent, and each one results inthe player being eq...
 7.7.4: If X and Y have joint density functionfX,Y(x, y) =%1/y, if 0 < y < ...
 7.7.5: The county hospital is located at the center of asquare whose sides...
 7.7.6: Afair die is rolled 10 times. Calculate the expectedsum of the 10 r...
 7.7.7: Suppose that A and B each randomly and independentlychoose 3 of 10 ...
 7.7.8: N people arrive separately to a professional dinner.Upon arrival, e...
 7.7.9: A total of n balls, numbered 1 through n, are putinto n urns, also ...
 7.7.10: Consider 3 trials, each having the same probabilityof success. Let ...
 7.7.11: Consider n independent flips of a coin havingprobability p of landi...
 7.7.12: A group of n men and n women is lined up atrandom.(a) Find the expe...
 7.7.13: A set of 1000 cards numbered 1 through 1000is randomly distributed ...
 7.7.14: An urn has m black balls. At each stage, a blackball is removed and...
 7.7.15: In Example 2h, say that i and j, i Z j, form amatched pair if i cho...
 7.7.16: Let Z be a standard normal random variable, and,for a fixed x, setX...
 7.7.17: A deck of n cards numbered 1 through n is thoroughlyshuffled so tha...
 7.7.18: Cards from an ordinary deck of 52 playing cardsare turned face up o...
 7.7.19: A certain region is inhabited by r distinct types ofa certain speci...
 7.7.20: In an urn containing n balls, the ith ball has weightW(i), i = 1, ....
 7.7.21: For a group of 100 people, compute(a) the expected number of days o...
 7.7.22: How many times would you expect to roll a fair diebefore all 6 side...
 7.7.23: Urn 1 contains 5 white and 6 black balls, while urn2 contains 8 whi...
 7.7.24: A bottle initially contains m large pills and n smallpills. Each da...
 7.7.25: Let X1,X2, . . . be a sequence of independent andidentically distri...
 7.7.26: If X1,X2, . . . ,Xn are independent and identicallydistributed rand...
 7.7.27: If 101 items are distributed among 10 boxes, thenat least one of th...
 7.7.28: The kofroutofn circular reliability system, k r n, consists of...
 7.7.29: There are 4 different types of coupons, the first2 of which compose...
 7.7.30: If X and Y are independent and identically distributedwith mean and...
 7.7.31: In 6, calculate the variance of the sum ofthe rolls.
 7.7.32: In 9, compute the variance of the numberof empty urns
 7.7.33: If E[X] = 1 andVar(X) = 5, find(a) E[(2 + X)2];(b) Var(4 + 3X).
 7.7.34: If 10 married couples are randomly seated at around table, compute ...
 7.7.35: Cards from an ordinary deck are turned face upone at a time. Comput...
 7.7.36: Let X be the number of 1s and Y the numberof 2s that occur in n rol...
 7.7.37: A die is rolled twice. Let X equal the sum of theoutcomes, and let ...
 7.7.38: The random variables X and Y have a joint densityfunction given byf...
 7.7.39: Let X1, . . . be independent with common mean and common variance 2...
 7.7.40: The joint density function of X and Y is given byf (x, y) = 1ye(y+x...
 7.7.41: Apond contains 100 fish, of which 30 are carp. If 20fish are caught...
 7.7.42: A group of 20 people consisting of 10 men and10 women is randomly a...
 7.7.43: Let X1,X2, . . . ,Xn be independent random variableshaving an unkno...
 7.7.44: Between two distinct methods for manufacturingcertain goods, the qu...
 7.7.45: If X1,X2,X3, and X4 are (pairwise) uncorrelatedrandom variables, ea...
 7.7.46: Consider the following dice game, as played at acertain gambling ca...
 7.7.47: Consider a graph having n vertices labeled1, 2, . . . , n, and supp...
 7.7.48: A fair die is successively rolled. Let X and Ydenote, respectively,...
 7.7.49: There are two misshapen coins in a box; theirprobabilities for land...
 7.7.50: The joint density of X and Y is given byf (x, y) = ex/yeyy, 0 < x <...
 7.7.51: The joint density of X and Y is given byf (x, y) = eyy, 0 < x < y, ...
 7.7.52: A population is made up of r disjoint subgroups.Let pi denote the p...
 7.7.53: A prisoner is trapped in a cell containing 3 doors.The first door l...
 7.7.54: Consider the following dice game: A pair of diceis rolled. If the s...
 7.7.55: Ten hunters are waiting for ducks to fly by. Whena flock of ducks f...
 7.7.56: The number of people who enter an elevator onthe ground floor is a ...
 7.7.57: Suppose that the expected number of accidents perweek at an industr...
 7.7.58: A coin having probability p of coming up heads iscontinually flippe...
 7.7.59: There are n + 1 participants in a game. Eachperson independently is...
 7.7.60: Each of m + 2 players pays 1 unit to a kitty inorder to play the fo...
 7.7.61: Let X1, . . . be independent random variables withthe common distri...
 7.7.62: Let U1,U2, . . . be a sequence of independent uniform(0, 1) random ...
 7.7.63: An urn contains 30 balls, of which 10 are red and8 are blue. From t...
 7.7.64: Type i light bulbs function for a random amountof time having mean ...
 7.7.65: The number of winter storms in a good year is aPoisson random varia...
 7.7.66: In Example 5c, compute the variance of the lengthof time until the ...
 7.7.67: Consider a gambler who, at each gamble, eitherwins or loses her bet...
 7.7.68: The number of accidents that a person has ina given year is a Poiss...
 7.7.69: Repeat when the proportion of thepopulation having a value of less ...
 7.7.70: Consider an urn containing a large number ofcoins, and suppose that...
 7.7.71: In 70, suppose that the coin is tossed ntimes. Let X denote the num...
 7.7.72: Suppose that in we continue to flip thecoin until a head appears. L...
 7.7.73: In Example 6b, let S denote the signal sent and Rthe signal receive...
 7.7.74: In Example 6c, suppose that X is uniformly distributedover (0, 1). ...
 7.7.75: The moment generating function of X is given byMX(t) = exp{2et 2} a...
 7.7.76: Let X be the value of the first die and Y the sum ofthe values when...
 7.7.77: The joint density of X and Y is given byf (x, y) = 1 2eye(xy)2/2 0 ...
 7.7.78: Two envelopes, each containing a check, areplaced in front of you. ...
 7.7.79: Successive weekly sales, in units of one thousanddollars, have a bi...
Solutions for Chapter 7: First Course in Probability 8th Edition
Full solutions for First Course in Probability  8th Edition
ISBN: 9780136033134
Solutions for Chapter 7
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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

Adjusted R 2
A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

Biased estimator
Unbiased estimator.

Bimodal distribution.
A distribution with two modes

Bivariate normal distribution
The joint distribution of two normal random variables

Completely randomized design (or experiment)
A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.

Components of variance
The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.

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

Conditional probability distribution
The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables

Continuous distribution
A probability distribution for a continuous random variable.

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 .

Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.

Distribution function
Another name for a cumulative distribution function.

Exhaustive
A property of a collection of events that indicates that their union equals the sample space.

Firstorder model
A model that contains only irstorder terms. For example, the irstorder response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irstorder model is also called a main effects model

Fisherâ€™s least signiicant difference (LSD) method
A series of pairwise hypothesis tests of treatment means in an experiment to determine which means differ.

Fixed factor (or fixed effect).
In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.

Fractional factorial experiment
A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.

Generator
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.

Harmonic mean
The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .