 2.2.1: Classify the following random variables as discrete or continuous: ...
 2.2.2: An overseas shipment of 5 foreign automobiles contains 2 that have ...
 2.2.3: Let W be a random variable giving the number of heads minus the num...
 2.2.4: A coin is flipped until 3 heads in succession occur. List only thos...
 2.2.5: Determine the value c so that each of the following functions can s...
 2.2.6: The shelf life, in days, for bottles of a certain prescribed medici...
 2.2.7: The total number of hours, measured in units of 100 hours, that a f...
 2.2.8: The proportion of people who respond to a certain mailorder solici...
 2.2.9: A shipment of 7 television sets contains 2 defective sets. A hotel ...
 2.2.10: An investment firm offers its customers municipal bonds that mature...
 2.2.11: The probability distribution of X, the number of imperfections per ...
 2.2.12: The waiting time, in hours, between successive speeders spotted by ...
 2.2.13: Find the cumulative distribution function of the random variable X ...
 2.2.14: Construct a graph of the cumulative distribution function of Exerci...
 2.2.15: Consider the density function f(x) = kx, 0 <x< 1, 0, elsewhere. (a)...
 2.2.16: Three cards are drawn in succession from a deck without replacement...
 2.2.17: From a box containing 4 dimes and 2 nickels, 3 coins are selected a...
 2.2.18: Find the probability distribution for the number of jazz CDs when 4...
 2.2.19: The time to failure in hours of an important piece of electronic eq...
 2.2.20: A cereal manufacturer is aware that the weight of the product in th...
 2.2.21: An important factor in solid missile fuel is the particle size dist...
 2.2.22: Measurements of scientific systems are always subject to variation,...
 2.2.23: Based on extensive testing, it is determined by the manufacturer of...
 2.2.24: The proportion of the budget for a certain type of industrial compa...
 2.2.25: Suppose a certain type of small data processing firm is so speciali...
 2.2.26: Magnetron tubes are produced on an automated assembly line. A sampl...
 2.2.27: Suppose it is known from large amounts of historical data that X, t...
 2.2.28: On a laboratory assignment, if the equipment is working, the densit...
 2.2.29: Determine the values of c so that the following functions represent...
 2.2.30: If the joint probability distribution of X and Y is given by f(x, y...
 2.2.31: From a sack of fruit containing 3 oranges, 2 apples, and 3 bananas,...
 2.2.32: A fastfood restaurant operates both a drivethrough facility and a ...
 2.2.33: A candy company distributes boxes of chocolates with a mixture of c...
 2.2.34: Let X and Y denote the lengths of life, in years, of two components...
 2.2.35: Let X denote the reaction time, in seconds, to a certain stimulus a...
 2.2.36: Each rear tire on an experimental airplane is supposed to be filled...
 2.2.37: Let X denote the diameter of an armored electric cable and Y denote...
 2.2.38: The amount of kerosene, in thousands of liters, in a tank at the be...
 2.2.39: Let X denote the number of times a certain numerical control machin...
 2.2.40: Suppose that X and Y have the following joint probability distribut...
 2.2.41: Given the joint density function f(x, y) = 6xy 8 , 0
 2.2.42: A coin is tossed twice. Let Z denote the number of heads on the fir...
 2.2.43: Determine whether the two random variables of Exercise 2.40 are dep...
 2.2.44: Determine whether the two random variables of Exercise 2.39 are dep...
 2.2.45: Let X, Y , and Z have the joint probability density function f(x, y...
 2.2.46: The joint density function of the random variables X and Y is f(x, ...
 2.2.47: Determine whether the two random variables of Exercise 2.35 are dep...
 2.2.48: The joint probability density function of the random variables X, Y...
 2.2.49: Determine whether the two random variables of Exercise 2.36 are dep...
 2.2.50: The probability distribution of the discrete random variable X is f...
 2.2.51: The probability distribution of X, the number of imperfections per ...
 2.2.52: A coin is biased such that a head is three times as likely to occur...
 2.2.53: Find the mean of the random variable T representing the total of th...
 2.2.54: In a gambling game, a woman is paid $3 if she draws a jack or a que...
 2.2.55: By investing in a particular stock, a person can make a profit in o...
 2.2.56: Suppose that an antique jewelry dealer is interested in purchasing ...
 2.2.57: The density function of coded measurements of the pitch diameter of...
 2.2.58: Two tirequality experts examine stacks of tires and assign a quali...
 2.2.59: The density function of the continuous random variable X, the total...
 2.2.60: If a dealers profit, in units of $5000, on a new automobile can be ...
 2.2.61: Assume that two random variables (X, Y ) are uniformly distributed ...
 2.2.62: Find the proportion X of individuals who can be expected to respond...
 2.2.63: Let X be a random variable with the following probability distribut...
 2.2.64: Suppose that you are inspecting a lot of 1000 light bulbs, among wh...
 2.2.65: A large industrial firm purchases several new word processors at th...
 2.2.66: The hospitalization period, in days, for patients following treatme...
 2.2.67: Suppose that X and Y have the following joint probability function:...
 2.2.68: Referring to the random variables whose joint probability distribut...
 2.2.69: In Exercise 2.19 on page 61, a density function is given for the ti...
 2.2.70: Let X and Y be random variables with joint density function f(x, y)...
 2.2.71: Exercise 2.21 on page 61 dealt with an important particle size dist...
 2.2.72: Consider the information in Exercise 2.20 on page 61. The problem d...
 2.2.73: Consider Exercise 2.24 on page 61. (a) What is the mean proportion ...
 2.2.74: In Exercise 2.23 on page 61, the distribution of times before a maj...
 2.2.75: In Exercise 2.11 on page 60, the distribution of the number of impe...
 2.2.76: Use Definition 2.16 on page 82 to find the variance of the random v...
 2.2.77: The random variable X, representing the number of errors per 100 li...
 2.2.78: Suppose that the probabilities are 0.4, 0.3, 0.2, and 0.1, respecti...
 2.2.79: A dealers profit, in units of $5000, on a new automobile is a rando...
 2.2.80: The proportion of people who respond to a certain mailorder solici...
 2.2.81: The total number of hours, in units of 100 hours, that a family run...
 2.2.82: Referring to Exercise 2.62 on page 80, find 2 g(X) for the function...
 2.2.83: The length of time, in minutes, for an airplane to obtain clearance...
 2.2.84: Find the covariance of the random variables X and Y of Exercise 2.3...
 2.2.85: For the random variables X and Y whose joint density function is gi...
 2.2.86: Given a random variable X, with standard deviation X, and a random ...
 2.2.87: Consider the situation in Exercise 2.75 on page 81. The distributio...
 2.2.88: For a laboratory assignment, if the equipment is working, the densi...
 2.2.89: For the random variables X and Y in Exercise 2.31 on page 72, deter...
 2.2.90: Random variables X and Y follow a joint distribution f(x, y) = 2, 0...
 2.2.91: Suppose that a grocery store purchases 5 cartons of skim milk at th...
 2.2.92: Repeat Exercise 2.83 on page 88 by applying Theorem 2.5 and Corolla...
 2.2.93: If a random variable X is defined such that E[(X 1)2 ] = 10 and E[(...
 2.2.94: The total time, measured in units of 100 hours, that a teenager run...
 2.2.95: Use Theorem 2.7 to evaluate E(2XY 2 X2Y ) for the joint probability...
 2.2.96: If X and Y are independent random variables with variances 2 X = 5 ...
 2.2.97: Repeat Exercise 2.96 if X and Y are not independent and XY = 1.
 2.2.98: Suppose that X and Y are independent random variables with probabil...
 2.2.99: Consider Review Exercise 2.117 on page 97. The random variables X a...
 2.2.100: Consider Review Exercise 2.106 on page 95. There are two service li...
 2.2.101: The length of time Y , in minutes, required to generate a human ref...
 2.2.102: A manufacturing company has developed a machine for cleaning carpet...
 2.2.103: A tobacco company produces blends of tobacco, with each blend conta...
 2.2.104: An insurance company offers its policyholders a number of different...
 2.2.105: Two electronic components of a missile system work in harmony for t...
 2.2.106: A service facility operates with two service lines. On a randomly s...
 2.2.107: Let the number of phone calls received by a switchboard during a 5...
 2.2.108: An industrial process manufactures items that can be classified as ...
 2.2.109: The life span in hours of an electrical component is a random varia...
 2.2.110: Pairs of pants are being produced by a particular outlet facility. ...
 2.2.111: The shelf life of a product is a random variable that is related to...
 2.2.112: Passenger congestion is a service problem in airports. Trains are i...
 2.2.113: Impurities in a batch of final product of a chemical process often ...
 2.2.114: The time Z in minutes between calls to an electrical supply system ...
 2.2.115: A chemical system that results from a chemical reaction has two imp...
 2.2.116: Consider the situation of Review Exercise 2.115. But suppose the jo...
 2.2.117: Consider the random variables X and Y that represent the number of ...
 2.2.118: The behavior of series of components plays a huge role in scientifi...
 2.2.119: Another type of system that is employed in engineering work is a gr...
 2.2.120: Consider a system of components in which there are 5 independent co...
 2.2.121: Project: Take 5 class periods to observe the shoe color of individu...
 2.2.122: Referring to the random variables whose joint probability density f...
 2.2.123: Assume the length X, in minutes, of a particular type of telephone ...
 2.2.124: Suppose it is known that the life X of a particular compressor, in ...
 2.2.125: Referring to the random variables whose joint density function is g...
 2.2.126: Show that Cov(aX, bY ) = ab Cov(X, Y ).
 2.2.127: Consider Exercise 2.58 on page 79. Can it be said that the ratings ...
 2.2.128: A companys marketing and accounting departments have determined tha...
 2.2.129: In a support system in the U.S. space program, a single crucial com...
 2.2.130: It is known through data collection and considerable research that ...
 2.2.131: A delivery truck travels from point A to point B and back using the...
 2.2.132: A convenience store has two separate locations where customers can ...
 2.2.133: As we shall illustrate in Chapter 7, statistical methods associated...
 2.2.134: Consider Review Exercise 2.113 on page 96. It involved Y , the prop...
 2.2.135: Project: Let X = number of hours each student in the class slept th...
Solutions for Chapter 2: Random Variables, Distributions and Expectations
Full solutions for Essentials of Probability & Statistics for Engineers & Scientists  1st Edition
ISBN: 9780321783738
Solutions for Chapter 2: Random Variables, Distributions and Expectations
Get Full SolutionsEssentials of Probability & Statistics for Engineers & Scientists was written by and is associated to the ISBN: 9780321783738. Since 135 problems in chapter 2: Random Variables, Distributions and Expectations have been answered, more than 15144 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Essentials of Probability & Statistics for Engineers & Scientists, edition: 1. Chapter 2: Random Variables, Distributions and Expectations includes 135 full stepbystep solutions.

2 k factorial experiment.
A full factorial experiment with k factors and all factors tested at only two levels (settings) each.

Analytic study
A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study

Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability

Bimodal distribution.
A distribution with two modes

Bivariate normal distribution
The joint distribution of two normal random variables

C chart
An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defectsperunit or U chart.

Combination.
A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.

Conditional variance.
The variance of the conditional probability distribution of a random variable.

Continuity correction.
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.

Correlation matrix
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 offdiagonal elements rij are the correlations between Xi and Xj .

Critical value(s)
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.

Defectsperunit control chart
See U chart

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

Designed experiment
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment

Discrete random variable
A random variable with a inite (or countably ininite) range.

Distribution function
Another name for a cumulative distribution function.

F distribution.
The distribution of the random variable deined as the ratio of two independent chisquare random variables, each divided by its number of degrees of freedom.

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.