 5.3.14: ?Double Jackpot Shawn lives near the border of Illinois and Missour...
 5.3.15: ?False Positives The ELISA is a test to determine whether the HIV a...
 5.3.16: ?Christmas Lights Christmas lights are often designed with a series...
 5.3.17: ?Life Expectancy The probability that a randomly selected 40yearo...
 5.3.18: ?Life Expectancy The probability that a randomly selected 40yearo...
 5.3.19: ?Derivatives In finance, a derivative is a financial asset whose va...
 5.3.20: ?Quality Control Suppose that a company selects two people who work...
 5.3.21: ?Reliability and Redundancy In airline applications, failure of a c...
 5.3.22: ?Reliability For a parallel structure of identical components, the ...
 5.3.23: ?Reliability and Redundancy, Part II See 21. Suppose a particular a...
 5.3.24: ?Cold Streaks Players in sports are said to have “hot streaks” and ...
 5.3.25: ?Bowling Suppose that Ralph gets a strike when bowling 30% of the t...
 5.3.26: ?Driving under the Influence Among 21 to 25yearolds, 29% say the...
 5.3.27: ?Defense System Suppose that a satellite defense system is establis...
 5.3.28: ?Audits and Pet Ownership According to Internal Revenue Service rec...
 5.3.29: ?Weight Gain and Gender According to the National Vital Statistics ...
 5.3.30: ?Stocks Suppose your financial advisor recommends three stocks to y...
 5.3.31: ?Betting on Sports According to a Gallup Poll, about 17% of adult A...
 5.3.32: ?Fingerprints Fingerprints are now widely accepted as a form of ide...
 5.3.33: ?You Explain It! Independence Suppose a mother already has three gi...
 5.3.34: ?You Explain It! Independence Ken and Dorothy like to fly to Colora...
 5.3.1: ?Two events E and F are _____ if the occurrence of event E in a pro...
 5.3.2: ?The word and in probability implies that we use the _____ Rule.
 5.3.3: ?The word or in probability implies that we use the _____ Rule.
 5.3.4: ?True or False: When two events are disjoint, they are also indepen...
 5.3.5: ?If two events E and F are independent, P(E and F) = _____ .
 5.3.6: ?Suppose events E and F are disjoint. What is P(E and F)?
 5.3.7: ?Determine whether the events E and F are independent or dependent....
 5.3.8: ?Determine whether the events E and F are independent or dependent....
 5.3.9: ?Suppose that events E and F are independent, P(E) = 0.3 and P(F) =...
 5.3.10: ?Suppose that events E and F are independent, P(E) = 0.7 and P(F) =...
 5.3.11: ?Flipping a Coin What is the probability of obtaining five heads in...
 5.3.12: ?Rolling a Die What is the probability of obtaining 4 ones in a row...
 5.3.13: ?Southpaws About 13% of the population is lefthanded. If two peopl...
Solutions for Chapter 5.3: Independence and the Multiplication Rule
Full solutions for Statistics: Informed Decisions Using Data  5th Edition
ISBN: 9780134133539
Solutions for Chapter 5.3: Independence and the Multiplication Rule
Get Full SolutionsSummary of Chapter 5.3: Independence and the Multiplication Rule
Identify independent events. Use the Multiplication Rule for Independent Events. Compute atleast probabilities
This textbook survival guide was created for the textbook: Statistics: Informed Decisions Using Data, edition: 5. This expansive textbook survival guide covers the following chapters and their solutions. Statistics: Informed Decisions Using Data was written by and is associated to the ISBN: 9780134133539. Chapter 5.3: Independence and the Multiplication Rule includes 34 full stepbystep solutions. Since 34 problems in chapter 5.3: Independence and the Multiplication Rule have been answered, more than 27069 students have viewed full stepbystep solutions from this chapter.

Alternative hypothesis
In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test

Analysis of variance (ANOVA)
A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation

Average
See Arithmetic mean.

Bayes’ theorem
An equation for a conditional probability such as PA B (  ) in terms of the reverse conditional probability PB A (  ).

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

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.

Conditional probability density function
The probability density function of the conditional probability distribution of a continuous random variable.

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).

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 .

Covariance matrix
A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the offdiagonal elements are the covariances between Xi and Xj . Also called the variancecovariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.

Defect
Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.

Defectsperunit control chart
See U chart

Design matrix
A matrix that provides the tests that are to be conducted in an experiment.

Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.

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).

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.

Gamma random variable
A random variable that generalizes an Erlang random variable to noninteger values of the parameter r

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

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 .