 2.5.1: Suppose that A, B, and D are any three events such that Pr(AD) Pr(...
 2.5.2: Suppose that a fair coin is tossed repeatedly and independently unt...
 2.5.3: Suppose that A and B are events such that Pr(A) = 1/3, Pr(B) = 1/5,...
 2.5.4: Suppose that A and B are independent events such that Pr(A) = 1/3 a...
 2.5.5: Suppose that in 10 rolls of a balanced die, the number 6 appeared e...
 2.5.6: Suppose that A, B, and D are events such that A and B are independe...
 2.5.7: Suppose that the events A, B, and C are mutually independent. Under...
 2.5.8: Suppose that the events A and B are disjoint and that each has posi...
 2.5.9: Suppose that A, B, and C are three events such that A and B are dis...
 2.5.10: Suppose that each of two dice is loaded so that when either die is ...
 2.5.11: Suppose that there is a probability of 1/50 that you will win a cer...
 2.5.12: Suppose that a balanced die is rolled three times, and let Xi denot...
 2.5.13: Three students A, B, and C are enrolled in the same class. Suppose ...
 2.5.14: Consider the World Series of baseball, as described in Exercise 16 ...
 2.5.15: Suppose that three red balls and three white balls are thrown at ra...
 2.5.16: If five balls are thrown at random into n boxes, and all throws are...
 2.5.17: Bus tickets in a certain city contain four numbers, U, V , W, and X...
 2.5.18: A certain group has eight members. In January, three members are se...
 2.5.19: For the conditions of Exercise 18, determine the probability that t...
 2.5.20: Suppose that two players A and B take turns rolling a pair of balan...
 2.5.21: Three players A, B, and C take turns tossing a fair coin. Suppose t...
 2.5.22: Suppose that a balanced die is rolled repeatedly until the same num...
 2.5.23: Suppose that 80 percent of all statisticians are shy, whereas only ...
 2.5.24: Dreamboat cars are produced at three different factories A, B, and ...
 2.5.25: Suppose that 30 percent of the bottles produced in a certain plant ...
 2.5.26: Suppose that a fair coin is tossed until a head is obtained and tha...
 2.5.27: Suppose that a family has exactly n children (n 2). Assume that the...
 2.5.28: Suppose that a fair coin is tossed independently n times. Determine...
 2.5.29: Suppose that 13 cards are selected at random from a regular deck of...
 2.5.30: Suppose that n letters are placed at random in n envelopes, as in t...
 2.5.31: Consider again the conditions of Exercise 30. Show that the probabi...
 2.5.32: Consider again the conditions of Exercise 7 of Sec. 2.2. If exactly...
 2.5.33: Consider again the conditions of Exercise 2 of Sec. 1.10. If a fami...
 2.5.34: Three prisoners A, B, and C on death row know that exactly two of t...
 2.5.35: Suppose that each of two gamblers A and B has an initial fortune of...
 2.5.36: A sequence of n job candidates is prepared to interview for a job. ...
Solutions for Chapter 2.5: Conditional Probability
Full solutions for Probability and Statistics  4th Edition
ISBN: 9780321500465
Solutions for Chapter 2.5: Conditional Probability
Get Full SolutionsProbability and Statistics was written by and is associated to the ISBN: 9780321500465. This textbook survival guide was created for the textbook: Probability and Statistics, edition: 4. Chapter 2.5: Conditional Probability includes 36 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 36 problems in chapter 2.5: Conditional Probability have been answered, more than 15908 students have viewed full stepbystep solutions from this chapter.

Additivity property of x 2
If two independent random variables X1 and X2 are distributed as chisquare with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chisquare random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chisquare random variables.

Alias
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

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

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

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

Average run length, or ARL
The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.

Box plot (or box and whisker plot)
A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).

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.

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

Chisquare test
Any test of signiicance based on the chisquare distribution. The most common chisquare tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data

Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.

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).

Counting techniques
Formulas used to determine the number of elements in sample spaces and events.

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

Deining relation
A subset of effects in a fractional factorial design that deine the aliases in the design.

Deming
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.

Dispersion
The amount of variability exhibited by data

Error mean square
The error sum of squares divided by its number of degrees of freedom.

Forward selection
A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.

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 .