- 13.5.1: Three concentric circles of radii 2, 3, and 4 are the boundaries of...
- 13.5.2: Using Monte Carlo procedure, write a program to estimate -(3) -(1) ...
- 13.5.3: In Buffons needle problem, let $ = 1 and d = 2, and use Monte Carlo...
Solutions for Chapter 13.5: Monte Carlo Method
Full solutions for Fundamentals of Probability, with Stochastic Processes | 3rd 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
Analysis of variance (ANOVA)
A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation
Asymptotic relative eficiency (ARE)
Used to compare hypothesis tests. The ARE of one test relative to another is the limiting ratio of the sample sizes necessary to obtain identical error probabilities for the two procedures.
A distribution with two modes
Binomial random variable
A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.
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).
Chi-square (or chi-squared) random variable
A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.
Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.
See Control chart.
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 .
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.
A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.
The response variable in regression or a designed experiment.
A probability distribution for a discrete random variable
Discrete random variable
A random variable with a inite (or countably ininite) range.
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.
A study in which a sample from a population is used to make inference to the population. See Analytic study
A property of a collection of events that indicates that their union equals the sample space.
A function used in the probability density function of a gamma random variable that can be considered to extend factorials