- 5.3.35: Consider a Poisson random variable withm 2.5. Use the Poisson formu...
- 5.3.36: Consider a Poisson random variable with m 3.Use the Poisson formula...
- 5.3.37: Consider a Poisson random variable with m 3.Use the Poisson formula...
- 5.3.38: Consider a Poisson random variable with m 0.8.Use Table 2 to find t...
- 5.3.39: Let x be a Poisson random variable with meanm 2. Calculate these pr...
- 5.3.40: Let x be a Poisson random variable with meanm 2.5. Use Table 2 in A...
- 5.3.41: Poisson vs. Binomial Let x be a binomial randomvariable with n 20 a...
- 5.3.42: Poisson vs. Binomial II To illustrate how wellthe Poisson probabili...
- 5.3.43: Airport Safety The increased number of smallcommuter planes in majo...
- 5.3.44: Intensive Care The number x of people enteringthe intensive care un...
- 5.3.45: Accident Prone According to a study conductedby the Department of P...
- 5.3.46: Accident Prone, continued Refer to Exercise5.45.a. Calculate the me...
- 5.3.47: Bacteria in Water Samples If a drop ofwater is placed on a slide an...
- 5.3.48: E. coli Outbreaks An outbreak of E. coli infectionsin August of 201...
Solutions for Chapter 5.3: The Poisson Probability Distribution
Full solutions for Introduction to Probability and Statistics 1 | 14th 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
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.
Attribute control chart
Any control chart for a discrete random variable. See Variables control chart.
See Arithmetic mean.
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).
A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.
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.
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.
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.
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.
Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.
A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).
A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the off-diagonal elements are the covariances between Xi and Xj . Also called the variance-covariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.
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.
Defects-per-unit control chart
See U chart
A probability distribution for a discrete random variable
The distribution of the random variable deined as the ratio of two independent chi-square random variables, each divided by its number of degrees of freedom.
A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function
Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.