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# Solutions for Chapter 4: Continuous Random Variables and Probability Distributions ## Full solutions for Probability and Statistics for Engineering and the Sciences (with Student Suite Online) | 7th Edition

ISBN: 9780495382171 Solutions for Chapter 4: Continuous Random Variables and Probability Distributions

Solutions for Chapter 4
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##### ISBN: 9780495382171

Probability and Statistics for Engineering and the Sciences (with Student Suite Online) was written by and is associated to the ISBN: 9780495382171. Chapter 4: Continuous Random Variables and Probability Distributions includes 128 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 128 problems in chapter 4: Continuous Random Variables and Probability Distributions have been answered, more than 20172 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Probability and Statistics for Engineering and the Sciences (with Student Suite Online), edition: 7.

Key Statistics Terms and definitions covered in this textbook
• 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

• Alias

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

• Biased estimator

Unbiased estimator.

• 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.

• Chi-square test

Any test of signiicance based on the chi-square distribution. The most common chi-square 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

• Conditional probability

The probability of an event given that the random experiment produces an outcome in another event.

• Consistent estimator

An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.

• Continuous random variable.

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

• Continuous uniform random variable

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

• 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).

• Defects-per-unit control chart

See U chart

• Design matrix

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

• Estimate (or point estimate)

The numerical value of a point estimator.

• Exhaustive

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

• Expected value

The expected value of a random variable X is its long-term 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.

• Finite population correction factor

A term in the formula for the variance of a hypergeometric random variable.

• 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.

• Gamma random variable

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

• Geometric random variable

A discrete random variable that is the number of Bernoulli trials until a success occurs.

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