- 6.3.1E: Some biology students were interested in analyzing the amount of ti...
- 6.3.2E: Let X equal the forced vital capacity (the volume of air a person c...
- 6.3.3E: Let Y1 < Y2 < Y3 < Y4 < Y5 be the order statistics of five independ...
- 6.3.4E: In the expression for gr(y) = G 'r (y) in Equation 6.3-1, let n = 6...
- 6.3.5E: Let Y1 < Y2 < · · · < Y8 be the order statistics of eight independe...
- 6.3.6E: Let W1 < W2 < · · · < Wn be the order statistics of n independent o...
- 6.3.7E: Let Y1 < Y2 < · · · < Y19 be the order statistics of n = 19 indepen...
- 6.3.8E: Let W1 < W2 < · · · < Wn be the order statistics of n independent o...
- 6.3.9E: Let Y1 < Y2 < · · · < Yn be the order statistics of a random sample...
- 6.3.10E: Use the heuristic argument to show that the joint pdf of the two or...
- 6.3.11E: Use the result of Exercise 6.3-10.(a) Find the joint pdf of Y1 and ...
- 184.108.40.206-1: Some biology students were interested in analyzing the amount of ti...
- 220.127.116.11-2: Let X equal the forced vital capacity (the volume of air a person c...
- 18.104.22.168-3: Let Y1 < Y2 < Y3 < Y4 < Y5 be the order statistics of five independ...
- 22.214.171.124-4: In the expression for gr(y) = G r(y) in Equation 6.3-1, let n = 6, ...
- 126.96.36.199-5: Let Y1 < Y2 < < Y8 be the order statistics of eight independent obs...
- 188.8.131.52-6: Let W1 < W2 < < Wn be the order statistics of n independent observa...
- 184.108.40.206-7: Let Y1 < Y2 < < Y19 be the order statistics of n = 19 independent o...
- 220.127.116.11-8: Let W1 < W2 < < Wn be the order statistics of n independent observa...
- 18.104.22.168-9: Let Y1 < Y2 < < Yn be the order statistics of a random sample of si...
- 22.214.171.124-10: Use the heuristic argument to show that the joint pdf of the two or...
- 126.96.36.199-11: Use the result of Exercise 6.3-10. (a) Find the joint pdf of Y1 and...
- 188.8.131.52-12: Nine measurements are taken on the strength of a certain metal. In ...
- 184.108.40.206-13: Some measurements (in mm) were made on specimens of the spider Sosi...
- 220.127.116.11-14: An interior automotive supplier places several electrical wires in ...
Solutions for Chapter 6.3: Point Estimation
Full solutions for Probability and Statistical Inference | 9th Edition
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
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
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.
A method of variable selection in regression that begins with all of the candidate regressor variables in the model and eliminates the insigniicant regressors one at a time until only signiicant regressors remain
An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).
Bivariate normal distribution
The joint distribution of two normal random variables
A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.
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 distribution
The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables
Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.
When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.
If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made
Another term for the conidence coeficient.
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.
A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.
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 .
Another name for factors that are arranged in a factorial experiment.
An expression sometimes used for nonlinear regression models or polynomial regression models.
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.
A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.