 9.9.1: Let Wn denote the st1rri of n, iridependent throws of a fair fo11r...
 9.9.2: Randorn variable J( has P JVIF Use cf> K ( s) to find the first , s...
 9.9.3: (A) Let K1, K2, ... , Krn be iid discrete uniforrr1 randorr1 variab...
 9.9.4: Let X1, X 2 , ... denote a sequer1ce of iid randorn variables \vit1...
 9.9.5: X rr1illisecor1ds, the total access tirr1e (waiting time + read tim...
 9.9.6: X is t11e binomial (100> 0.5) randorn variable and y is the discret...
 9.9.7: X 1 and X 2 are iid random variables 'vith variance Var[X ]. (a) Wh...
 9.9.8: F lip a biased coin 100 times. On each flip, P [H ] = p. Let X i de...
 9.9.9: A radio program gives concert tickets to the fourth caller with the...
 9.9.10: X1, X2 and X3 are iid continuous unifo1m random variables. Random v...
 9.9.11: Random variables X and Y have joint PDF f ( ) {2 x>O,y>O,: : e+y<l,...
 9.9.12: For a constant a > 0, a Laplace random variable X has PDF j. ( ) a ...
 9.9.13: Random variables ,J and K have the joint probability mass function ...
 9.9.14: X is the continuous uniform (a,b) random variable. F ind the MGF </...
 9.9.15: Let X be a Gaussian (0, a) random variable. Use the moment generati...
 9.9.16: Random variable K has a discrete uniform (1,n ,) P lVIF. Use the MG...
 9.9.17: N is the binomial (100, 0.4) random variable. M is the binomial (50...
 9.9.18: Random variable Y has the moment generating function <f>y(s) = 1/(1...
 9.9.19: Let Ki, 1<2, . .. denote a sequence of iid Bernoulli (p) random var...
 9.9.20: Suppose you participate in a chess tournament in which you play n, ...
 9.9.21: At time t = 0, you begin counting the arrivals of buses at a depot....
 9.9.22: Suppose that during the ith day of December, the energy Xi stored b...
 9.9.23: 1{, 1<1 , K2 , . . . are iid random variables. Use the ~!IGF of JV!...
 9.9.24: X1, X2, .. . is a sequence of iid random variables each with expone...
 9.9.25: In any game, the number of passes N that Donovan ~1cNabb 'vill thro...
 9.9.26: Suppose we flip a fair coin repeatedly. Let xi equal 1 if flip i 'V...
 9.9.27: K , the number of passes that Donovan ~1cNabb completes in any game...
 9.9.28: This problem continues the lottery of 3.7.10 in 'vhich each ticket ...
 9.9.29: Xis the Gaussian (1, 1) random variable and J{ is a discrete random...
 9.9.30: Let X 1, ... , X n denote a sequence of iid Bernoulli (p) random va...
 9.9.31: Suppose you participate in a chess tournament in which you play unt...
 9.9.32: The 'vaiting time in milliseconds, vV, for accessing one record fro...
 9.9.33: Internet packets can be classified as video ('! ) or as generic dat...
 9.9.34: The duration of a cellular telephone call is an exponential random ...
 9.9.35: Let 1<1, K2, .. . be an iid sequence of Poisson (1) random variable...
 9.9.36: In any oneminute interval, the number of requests for a popular \i...
 9.9.37: Integrated circuits from a certain factory pass a certain quality t...
 9.9.38: Internet packets can1 be classified as video (V ) or as generic dat...
 9.9.39: In the presence of a head,vind of normalized intensity vV, your spe...
 9.9.40: An amplifier circuit has po,ver consumption Y that gro,vs nonlinear...
 9.9.41: In the face of perpetually varying headwinds, cyclists Lance and As...
 9.9.42: Suppose your grade in a probability course depends on 10 weekly qui...
 9.9.43: Wn is the number of ones in 1071 independent transmitted bits, each...
 9.9.44: use the l\IIATLAB plot function to compare the Erlang (n, >.) PDF t...
 9.9.45: Recreate the plots of Figure 9.3. On the same plots, superimpose th...
 9.9.46: Find the P~1F of W = X 1 + X 2 in Exa1n ple 9 .1 7 using the conv f...
 9.9.47: use unif orrn12. rn to estimate the probability of a storm surge gr...
 9.9.48: X1, X2, and X3 are independent random variables such that X k has P...
 9.9.49: Let X and Y denote independent finite random variables described by...
Solutions for Chapter 9: Sums of Random Variables
Full solutions for Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers  3rd Edition
ISBN: 9781118324561
Solutions for Chapter 9: Sums of Random Variables
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 49 problems in chapter 9: Sums of Random Variables have been answered, more than 11174 students have viewed full stepbystep solutions from this chapter. Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers was written by and is associated to the ISBN: 9781118324561. This textbook survival guide was created for the textbook: Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers, edition: 3. Chapter 9: Sums of Random Variables includes 49 full stepbystep solutions.

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

Assignable cause
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.

Attribute control chart
Any control chart for a discrete random variable. See Variables control chart.

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.

Bivariate normal distribution
The joint distribution of two normal random variables

Block
In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.

Central composite design (CCD)
A secondorder response surface design in k variables consisting of a twolevel factorial, 2k axial runs, and one or more center points. The twolevel factorial portion of a CCD can be a fractional factorial design when k is large. The CCD is the most widely used design for itting a secondorder model.

Chisquare (or chisquared) 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.

Chisquare test
Any test of signiicance based on the chisquare distribution. The most common chisquare 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

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

Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.

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

Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.

Crossed factors
Another name for factors that are arranged in a factorial experiment.

Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.

Event
A subset of a sample space.

Ftest
Any test of signiicance involving the F distribution. The most common Ftests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.

Fraction defective control chart
See P chart

Hat matrix.
In multiple regression, the matrix H XXX X = ( ) ? ? 1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .