- 4.2.1: Suppose that the return R (in dollars per share) of a stock has the...
- 4.2.2: Suppose that three random variables X1, X2, X3 form a random sample...
- 4.2.3: Suppose that three random variables X1, X2, X3 form a random sample...
- 4.2.4: Suppose that the random variable X has the uniform distribution on ...
- 4.2.5: Suppose that the random variable X has the uniform distribution on ...
- 4.2.6: Suppose that a particle starts at the origin of the real line and m...
- 4.2.7: Suppose that on each play of a certain game a gambler is equally li...
- 4.2.8: Suppose that a class contains 10 boys and 15 girls, and suppose tha...
- 4.2.9: Suppose that the proportion of defective items in a large lot is p,...
- 4.2.10: Suppose that a fair coin is tossed repeatedly until a head is obtai...
- 4.2.11: Suppose that a fair coin is tossed repeatedly until exactly k heads...
- 4.2.12: Suppose that the two return random variables R1 and R2 in Examples ...
- 4.2.13: Prove the special case of Theorem 4.2.5 in which the function g is ...
Solutions for Chapter 4.2: Expectation
Full solutions for Probability and Statistics | 4th Edition
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
Attribute control chart
Any control chart for a discrete random variable. See Variables control chart.
An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.
See Control chart.
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 .
A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the off-diagonal elements rij are the correlations between Xi and Xj .
Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.
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.
Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.
Another name for a probability density function
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.
Error mean square
The error sum of squares divided by its number of degrees of freedom.
The variance of an error term or component in a model.
The distribution of the random variable deined as the ratio of two independent chi-square random variables, each divided by its number of degrees of freedom.
Any test of signiicance involving the F distribution. The most common F-tests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.
Fraction defective control chart
See P chart
In multiple regression, the matrix H XXX X = ( ) ? ? -1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .