 1.4.1E: Let A and B be independent events with P(A) =0.7 and P(B) = 0.2. Co...
 1.4.2E: Let P(A) = 0.3 and P(B) = 0.6.(a) Find P(A ? B) when A and B are in...
 1.4.3E: Let A and B be independent events with P(A) = 1/4 and P(B) = 2/3. C...
 1.4.4E: Prove parts (b) and (c) of Theorem 1.41.
 1.4.5E: If P(A) = 0.8, P(B) = 0.5, and P(A ? B) = 0.9, are A and B independ...
 1.4.6E: Show that if A, B, and C are mutually independent, then the followi...
 1.4.7E: Each of three football players will attempt to kick a field goal fr...
 1.4.8E: Die A has orange on one face and blue on five faces, Die B has oran...
 1.4.9E: Suppose that A, B, and C are mutually independent events and that P...
 1.4.10E: Let D1, D2, D3 be three foursided dice whose sides have been label...
 1.4.11E: Let A and B be two events.(a) If the events A and B are mutually ex...
 1.4.12E: Flip an unbiased coin five independent times. Compute the probabili...
 1.4.13E: An urn contains two red balls and four white balls. Sample successi...
 1.4.14E: In Example 1.45, suppose that the probability of failure of a comp...
 1.4.16E: An urn contains five balls, one marked WIN and four marked LOSE. Yo...
 1.4.17E: Each of the 12 students in a class is given a fair 12sided die. In...
 1.4.19E: Extend Example 1.46 to an nsided die. That is, suppose that a fai...
 1.4.1.41: Let A and B be independent events with P(A) = 0.7 and P(B) = 0.2. C...
 1.4.1.42: Let P(A) = 0.3 and P(B) = 0.6. (a) Find P(A B) when A and B are ind...
 1.4.1.43: Let A and B be independent events with P(A) = 1/4 and P(B) = 2/3. C...
 1.4.1.44: Prove parts (b) and (c) of Theorem 1.41.
 1.4.1.45: If P(A) = 0.8, P(B) = 0.5, and P(A B) = 0.9, are A and B independen...
 1.4.1.46: Show that if A, B, and C are mutually independent, then the followi...
 1.4.1.47: Each of three football players will attempt to kick a field goal fr...
 1.4.1.48: Die A has orange on one face and blue on five faces, Die B has oran...
 1.4.1.49: Suppose that A, B, and C are mutually independent events and that P...
 1.4.1.410: Let D1, D2, D3 be three foursided dice whose sides have been label...
 1.4.1.411: Let A and B be two events. (a) If the events A and B are mutually e...
 1.4.1.412: Flip an unbiased coin five independent times. Compute the probabili...
 1.4.1.413: An urn contains two red balls and four white balls. Sample successi...
 1.4.1.414: In Example 1.45, suppose that the probability of failure of a comp...
 1.4.1.415: An urn contains 10 red and 10 white balls. The balls are drawn from...
 1.4.1.416: An urn contains five balls, one marked WIN and four marked LOSE. Yo...
 1.4.1.417: Each of the 12 students in a class is given a fair 12sided die. In...
 1.4.1.418: An eightteam singleelimination tournament is set up as follows:Fo...
 1.4.1.419: Extend Example 1.46 to an nsided die. That is, suppose that a fai...
 1.4.1.420: Hunters A and B shoot at a target with probabilities of p1 and p2, ...
Solutions for Chapter 1.4: Probability
Full solutions for Probability and Statistical Inference  9th Edition
ISBN: 9780321923271
Solutions for Chapter 1.4: Probability
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Probability and Statistical Inference , edition: 9th. Since 37 problems in chapter 1.4: Probability have been answered, more than 35074 students have viewed full stepbystep solutions from this chapter. Probability and Statistical Inference was written by Sieva Kozinsky and is associated to the ISBN: 9780321923271. Chapter 1.4: Probability includes 37 full stepbystep solutions.

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.

Biased estimator
Unbiased estimator.

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).

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

Causal variable
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable

Central limit theorem
The simplest form of the central limit theorem states that the sum of n independently distributed random variables will tend to be normally distributed as n becomes large. It is a necessary and suficient condition that none of the variances of the individual random variables are large in comparison to their sum. There are more general forms of the central theorem that allow ininite variances and correlated random variables, and there is a multivariate version of the theorem.

Chance cause
The portion of the variability in a set of observations that is due to only random forces and which cannot be traced to speciic sources, such as operators, materials, or equipment. Also called a common cause.

Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.

Correlation
In the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks.

Critical value(s)
The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. 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.

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

Density function
Another name for a probability density function

Eficiency
A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.

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

Finite population correction factor
A term in the formula for the variance of a hypergeometric random variable.

Fraction defective control chart
See P chart

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.
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