- 10.4.1: A fair coin is tossed until two tails occur successively. Find the ...
- 10.4.2: The orders received for grain by a farmer add up to X tons, where X...
- 10.4.3: In a box, Lynn has b batteries of which d are dead. She tests them ...
- 10.4.4: For given random variables Y and Z, let X = B Y with probability p ...
- 10.4.5: A typist, on average, makes three typing errors in every two pages....
- 10.4.6: In data communication, usually messages sent are combinations of ch...
- 10.4.7: From an ordinary deck of 52 cards, cards are drawn at random, one b...
- 10.4.8: Suppose that X and Y are independent random variables with probabil...
- 10.4.9: Prove that, for a Poisson random variable N, if the parameter is no...
- 10.4.10: Suppose that X and Y represent the amount of money in the wallets o...
- 10.4.11: A fair coin is tossed successively. Let Kn be the number of tosses ...
- 10.4.12: In Rome, tourists arrive at a historical monument according to a Po...
- 10.4.13: During an academic year, the admissions office of a small college r...
- 10.4.14: Each time that Steven calls his friend Adam, the probability that A...
- 10.4.15: Recently, Larry taught his daughter Emily how to play backgammon. T...
- 10.4.16: (Genetics) Hemophilia is a sex-linked disease with normal allele H ...
- 10.4.17: A spice company distributes cinnamon in one-pound bags. Suppose tha...
- 10.4.18: Suppose that a device is powered by a battery. Since an uninterrupt...
- 10.4.19: Let X and Y be continuous random variables. Prove that E 4!X E(X|Y ...
- 10.4.20: Let X and Y be two given random variables. Prove that Var(X|Y ) = E...
- 10.4.21: Prove Theorem 10.8.
Solutions for Chapter 10.4: Conditioning on Random Variables
Full solutions for Fundamentals of Probability, with Stochastic Processes | 3rd Edition
a-error (or a-risk)
In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).
Adjusted R 2
A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
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
The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.
An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).
A distribution with two modes
Box plot (or box and whisker plot)
A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).
An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defects-per-unit or U chart.
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.
Components of variance
The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.
Conditional probability density function
The probability density function of the conditional probability distribution of a continuous random variable.
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.
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.
The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.
Cumulative sum control chart (CUSUM)
A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t
Defects-per-unit control chart
See U chart
A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.
Error mean square
The error sum of squares divided by its number of degrees of freedom.
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.
Estimator (or point estimator)
A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.