- 5.2.1: Jim buys 60 lottery tickets every week. If only 5% of the lottery t...
- 5.2.2: Suppose that 3% of the families in a large city have an annual inco...
- 5.2.3: Suppose that 2.5% of the population of a border town are illegal im...
- 5.2.4: By Example 2.21, the probability that a poker hand is a full house ...
- 5.2.5: On a random day, the number of vacant rooms of a big hotel in New Y...
- 5.2.6: On average, there are three misprints in every 10 pages of a partic...
- 5.2.7: Suppose that X is a Poisson random variable with P (X = 1) = P (X =...
- 5.2.8: Suppose that n raisins have been carefully mixed with a batch of do...
- 5.2.9: The children in a small town all own slingshots. In a recent contes...
- 5.2.10: The department of mathematics of a state university has 26 faculty ...
- 5.2.11: Suppose that on a summer evening, shooting stars are observed at a ...
- 5.2.12: Suppose that in Japan earthquakes occur at a Poisson rate of three ...
- 5.2.13: Suppose that, for a telephone subscriber, the number of wrong numbe...
- 5.2.14: In a certain town, crimes occur at a Poisson rate of five per month...
- 5.2.15: Accidents occur at an intersection at a Poisson rate of three per d...
- 5.2.16: Customers arrive at a bookstore at a Poisson rate of six per hour. ...
- 5.2.17: A wire manufacturing company has inspectors to examine the wire for...
- 5.2.18: On a certain two-lane north-south highway, there is a T junction. C...
- 5.2.19: Suppose that, on the Richter scale, earthquakes of magnitude 5.5 or...
- 5.2.20: According to the United States Postal Service, http:www.usps.gov, M...
- 5.2.21: Suppose that in Maryland, on a certain day, N lottery tickets are s...
- 5.2.22: Balls numbered 1,2, ... , and n are randomly placed into cells numb...
- 5.2.23: Let $ N (t), t 0 % be a Poisson process. What is the probability of...
- 5.2.24: Let $ N (t), t 0 % be a Poisson process with rate . Suppose that N ...
- 5.2.25: Customers arrive at a grocery store at a Poisson rate of one per mi...
- 5.2.26: In a forest, the number of trees that grow in a region of area R ha...
- 5.2.27: Let X be a Poisson random variable with parameter . Show that the m...
Solutions for Chapter 5.2: Poisson Random Variables
Full solutions for Fundamentals of Probability, with Stochastic Processes | 3rd Edition
2 k factorial experiment.
A full factorial experiment with k factors and all factors tested at only two levels (settings) each.
2 k p - factorial experiment
A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each
All possible (subsets) regressions
A method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions
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 arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average
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.
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.
See Arithmetic mean.
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.
A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.
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.
Any test of signiicance based on the chi-square distribution. The most common chi-square tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data
An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.
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.
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.
Deming’s 14 points.
A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment
The variance of an error term or component in a model.
Fraction defective control chart
See P chart
Goodness of fit
In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.