 6.6.1: Two fair dice are rolled. Find the joint probabilitymass function o...
 6.6.2: Suppose that 3 balls are chosen without replacementfrom an urn cons...
 6.6.3: In 2, suppose that the white balls arenumbered, and let Yi equal 1 ...
 6.6.4: Repeat when the ball selected isreplaced in the urn before the next...
 6.6.5: Repeat when the ball selected isreplaced in the urn before the next...
 6.6.6: A bin of 5 transistors is known to contain 2 thatare defective. The...
 6.6.7: Consider a sequence of independent Bernoulli trials,each of which i...
 6.6.8: The joint probability density function of X and Yis given byf (x, y...
 6.6.9: The joint probability density function of X and Yis given byf (x, y...
 6.6.10: The joint probability density function of X and Yis given byf (x, y...
 6.6.11: A television store owner figures that 45 percent ofthe customers en...
 6.6.12: The number of people that enter a drugstore ina given hour is a Poi...
 6.6.13: A man and a woman agree to meet at a certainlocation about 12:30 P....
 6.6.14: An ambulance travels back and forth at a constantspeed along a road...
 6.6.15: The random vector (X, Y) is said to be uniformlydistributed over a ...
 6.6.16: Suppose that n points are independently chosen atrandom on the circ...
 6.6.17: Three points X1,X2,X3 are selected at randomon a line L. What is th...
 6.6.18: Three points X1,X2,X3 are selected at randomon a line L. What is th...
 6.6.19: Show that f (x, y) = 1/x, 0 < y < x < 1, is a jointdensity function...
 6.6.20: The joint density of X and Y is given byf (x, y) =0xe(x+y) x > 0, y...
 6.6.21: Letf (x, y) = 24xy 0 x 1, 0 y 1, 0 x + y 1and let it equal 0 otherw...
 6.6.22: The joint density function of X and Y isf (x, y) =%x + y 0 < x < 1,...
 6.6.23: The random variables X and Y have joint densityfunctionf (x, y) = 1...
 6.6.24: Consider independent trials, each of which resultsin outcome i, i =...
 6.6.25: Suppose that 106 people arrive at a service stationat times that ar...
 6.6.26: Suppose that A, B, C, are independent randomvariables, each being u...
 6.6.27: If X1 and X2 are independent exponential randomvariables with respe...
 6.6.28: The time that it takes to service a car is an exponentialrandom var...
 6.6.29: The gross weekly sales at a certain restaurant isa normal random va...
 6.6.30: Jills bowling scores are approximately normallydistributed with mea...
 6.6.31: According to the U.S. National Center for HealthStatistics, 25.2 pe...
 6.6.32: The expected number of typographical errors on apage of a certain m...
 6.6.33: The monthly worldwide average number of airplanecrashes of commerci...
 6.6.34: Jay has two jobs to do, one after the other. Eachattempt at job i t...
 6.6.35: In 4, calculate the conditional probabilitymass function of X1 give...
 6.6.36: In 3, calculate the conditional probabilitymass function of Y1 give...
 6.6.37: In 5, calculate the conditional probabilitymass function of Y1 give...
 6.6.38: Choose a number X at random from the set ofnumbers {1, 2, 3, 4, 5}....
 6.6.39: Two dice are rolled. Let X and Y denote, respectively,the largest a...
 6.6.40: The joint probability mass function of X and Y isgiven byp(1, 1) = ...
 6.6.41: The joint density function of X and Y is given byf (x, y) = xex(y+1...
 6.6.42: The joint density of X and Y isf (x, y) = c(x2 y2)ex 0 x < q, x y x...
 6.6.43: An insurance company supposes that each personhas an accident param...
 6.6.44: If X1,X2,X3 are independent random variablesthat are uniformly dist...
 6.6.45: A complex machine is able to operate effectivelyas long as at least...
 6.6.46: If 3 trucks break down at points randomly distributedon a road of l...
 6.6.47: Consider a sample of size 5 from a uniform distributionover (0, 1)....
 6.6.48: If X1,X2,X3,X4,X5 are independent and identicallydistributed expone...
 6.6.49: Let X(1),X(2), . . . ,X(n) be the order statisticsof a set of n ind...
 6.6.50: Let Z1 and Z2 be independent standard normalrandom variables. Show ...
 6.6.51: Derive the distribution of the range of a sample ofsize 2 from a di...
 6.6.52: Let X and Y denote the coordinates of a point uniformlychosen in th...
 6.6.53: If X and Y are independent random variablesboth uniformly distribut...
 6.6.54: If U is uniform on (0, 2) and Z, independent ofU, is exponential wi...
 6.6.55: X and Y have joint density functionf (x, y) = 1x2y2 x 1, y 1(a) Com...
 6.6.56: If X and Y are independent and identically distributeduniform rando...
 6.6.57: Repeat 6.56 when X and Y are independentexponential random variable...
 6.6.58: If X1 and X2 are independent exponential randomvariables, each havi...
 6.6.59: If X, Y, and Z are independent random variableshaving identical den...
 6.6.60: In Example 8b, let Yk+1 = n + 1 ki=1Yi. Showthat Y1, . . . ,Yk,Yk+1...
 6.6.61: Consider an urn containing n balls numbered1, . . . , n, and suppos...
Solutions for Chapter 6: First Course in Probability 8th Edition
Full solutions for First Course in Probability  8th Edition
ISBN: 9780136033134
Solutions for Chapter 6
Get Full SolutionsThis textbook survival guide was created for the textbook: First Course in Probability, edition: 8. First Course in Probability was written by Sieva Kozinsky and is associated to the ISBN: 9780136033134. Since 61 problems in chapter 6 have been answered, more than 3253 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 6 includes 61 full stepbystep solutions.

2 k p  factorial experiment
A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each

`error (or `risk)
In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).

Addition rule
A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).

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

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

Biased estimator
Unbiased estimator.

C chart
An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defectsperunit or U chart.

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

Conidence interval
If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made

Control limits
See Control chart.

Correction factor
A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .

Correlation coeficient
A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).

Degrees of freedom.
The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.

Distribution free method(s)
Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).

Distribution function
Another name for a cumulative distribution function.

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

Error variance
The variance of an error term or component in a model.

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.

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.

Goodness of fit
In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.
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