 7.2.1: It takes a professor a random time between 20 and 27 minutes to wal...
 7.2.2: Suppose that 15 points are selected at random and independently fro...
 7.2.3: The time at which a bus arrives at a station is uniform over an int...
 7.2.4: Suppose that b is a random number from the interval (3, 3). What is...
 7.2.5: The radius of a sphere is a random number between 2 and 4. What is ...
 7.2.6: A point is selected at random on a line segment of length $. What i...
 7.2.7: A point is selected at random on a line segment of length $. What i...
 7.2.8: From the class of all triangles one is selected at random. What is ...
 7.2.9: A farmer who has two pieces of lumber of lengths a and b (a < b) de...
 7.2.10: Let be a random number between /2 and /2. Find the probability dens...
 7.2.11: Let X be a random number from [0, 1]. Find the probability mass fun...
 7.2.12: Let X be a random number from (0, 1). Find the density functions of...
 7.2.13: Let X be a uniform random variable over the interval (0, 1+), where...
 7.2.14: Let X be a continuous random variable with distribution function F....
 7.2.15: Let g be a nonnegative realvalued function on R that satisfies the...
 7.2.16: The sample space of an experiment is S = (0, 1), and for every subs...
 7.2.17: Let Y be a random number from (0, 1). Let X be the second digit of ...
 7.2.18: Find the expected value and the variance of a random variable with ...
 7.2.19: Let X N (, 2). Find the probability distribution function of X  a...
 7.2.20: Determine the value(s) of k for which the following is the probabil...
 7.2.21: The viscosity of a brand of motor oil is normal with mean 37 and st...
 7.2.22: In a certain town the length of residence of a family in a home is ...
 7.2.23: Let (,) and Z N (0, 1); find E(eZ).
 7.2.24: Let X N (0, 2). Calculate the density function of Y = X2.
 7.2.25: Let X N (, 2). Calculate the density function of Y = eX.
 7.2.26: Let X N (0, 1). Calculate the density function of Y = X.
 7.2.27: Suppose that the odds are 1 to 5000 in favor of a customer of a par...
 7.2.28: Every day a factory produces 5000 light bulbs, of which 2500 are ty...
 7.2.29: To examine the accuracy of an algorithm that selects random numbers...
 7.2.30: Prove that for some constant k, f (x) = kax2 , a (0,), is a normal ...
 7.2.31: (a) Prove that for all x > 0, 1 x 2 * 1 1 x2 , ex2/2 < 1 (x) < 1 x...
 7.2.32: Let Z be a standard normal random variable. Show that for x > 0, li...
 7.2.33: The amount of soft drink in a bottle is a normal random variable. S...
 7.2.34: The amount of soft drink in a bottle is a normal random variable. S...
 7.2.35: In a forest, the number of trees that grow in a region of area R ha...
 7.2.36: Let I = # 0 ex2/2 dx; then I 2 = E 0 8 E 0 e(x2+y2)/2 dy9 dx. Let y...
Solutions for Chapter 7.2: Normal Random Variables
Full solutions for Fundamentals of Probability, with Stochastic Processes  3rd Edition
ISBN: 9780131453401
Solutions for Chapter 7.2: Normal Random Variables
Get Full SolutionsFundamentals of Probability, with Stochastic Processes was written by and is associated to the ISBN: 9780131453401. This textbook survival guide was created for the textbook: Fundamentals of Probability, with Stochastic Processes, edition: 3. Chapter 7.2: Normal Random Variables includes 36 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 36 problems in chapter 7.2: Normal Random Variables have been answered, more than 13904 students have viewed full stepbystep solutions from this chapter.

`error (or `risk)
In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).

Alias
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

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.

Comparative experiment
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.

Conditional probability density function
The probability density function of the conditional probability distribution of a continuous random variable.

Consistent estimator
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.

Continuous distribution
A probability distribution for a continuous random variable.

Control limits
See Control chart.

Correction factor
A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .

Correlation coeficient
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).

Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.

Defectsperunit control chart
See U chart

Design matrix
A matrix that provides the tests that are to be conducted in an experiment.

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).

Distribution function
Another name for a cumulative distribution function.

Enumerative study
A study in which a sample from a population is used to make inference to the population. See Analytic study

Error of estimation
The difference between an estimated value and the true value.

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 modelitting process and not on replication.

Fractional factorial experiment
A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.