- 4-5.1: Selecting Cards Find the probability of getting 2 face cards (king,...
- 4-5.2: Selecting a Committee A parent-teacher committee consisting of 4 pe...
- 4-5.3: Management Seminar In a company there are 7 executives: 4 women and...
- 4-5.4: Senate Partisanship The composition of the Senate of the 111th Cong...
- 4-5.5: Congressional Committee Memberships The composition of the 108th Co...
- 4-5.6: Defective Resistors A package contains 12 resistors, 3 of which are...
- 4-5.7: Winning Tickets If 50 tickets are sold and 2 prizes are to be award...
- 4-5.8: Getting a Full House Find the probability of getting a full house (...
- 4-5.9: Flight School Graduation At a recent graduation at a naval flight s...
- 4-5.10: Selecting Cards The red face cards and the black cards numbered 29 ...
- 4-5.11: Socks in a Drawer A drawer contains 11 identical red socks and 8 id...
- 4-5.12: Selecting Books Find the probability of selecting 3 science books a...
- 4-5.13: Rolling Three Dice When 3 dice are rolled, find the probability of ...
- 4-5.14: Football Team Selection A football team consists of 20 each freshme...
- 4-5.15: Arrangement of Washers Find the probability that if 5 different-siz...
- 4-5.16: Using the information in Exercise 63 in Section 44, find the probab...
- 4-5.17: Plant Selection All holly plants are dioeciousa male plant must be ...
Solutions for Chapter 4-5: Probability and Counting Rules
Full solutions for Elementary Statistics: A Step by Step Approach 8th ed. | 8th Edition
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.
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.
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.
The tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.
A probability distribution for a continuous random variable.
A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.
Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.
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.
The amount of variability exhibited by data
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 sum of squares
In analysis of variance, this is the portion of total variability that is due to the random component in the data. It is usually based on replication of observations at certain treatment combinations in the experiment. It is sometimes called the residual sum of squares, although this is really a better term to use only when the sum of squares is based on the remnants of a model-itting process and not on replication.
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.
In statistical quality control, that portion of a number of units or the output of a process that is defective.