 2.2.1.1: An ofce has four copying machines, and the random variable X measur...
 2.2.1.2: Figure 2.18 presents the cumulative distribution function of a rand...
 2.2.1.3: Suppose that two fair dice are rolled and that the two numbers reco...
 2.2.1.4: Two cards are drawn at random from a pack of cards with replacement...
 2.2.1.5: Two fair dice, one red and one blue, are rolled. A score is calcula...
 2.2.1.6: A fair coin is tossed three times. A player wins $1 if the rst toss...
 2.2.1.7: Consider Example 5 and the probability values given in Figure 1.38....
 2.2.1.8: Four cards are labeled $1, $2, $3, and $6. A player pays $4, select...
 2.2.1.9: A company has ve warehouses, only two of which have a particular pr...
 2.2.1.10: Suppose that a random variable X can take the value 1, 2, or any ot...
 2.2.1.11: A consultant has six appointment times that are open, three on Mond...
 2.2.2.1: Consider a random variable measuring the following quantities. In e...
 2.2.2.2: A random variable X takes values between 4 and 6 with a probability...
 2.2.2.3: A random variable X takes values between2 and 3 with a probability ...
 2.2.2.4: A random variable X takes values between 0 and 4 with a cumulative ...
 2.2.2.5: A random variable X takes values between 0 andwith a cumulative dis...
 2.2.2.6: A car panel is spraypainted by a machine, and the technicians are ...
 2.2.2.7: Suppose that the random variable X is the time taken by a garagetos...
 2.2.2.8: The bending capabilities of plastic sheets are investigated by bend...
 2.2.2.9: An archer shoots an arrow at a circular target with a radius of 50 ...
 2.2.2.10: Sometimes a random variable is a mix of discrete and continuous com...
 2.2.2.11: The resistance X of an electrical component has a probability densi...
 2.2.3.1: Consider again the four copying machines discussed in 2.1.1. What i...
 2.2.3.2: Consider again 2.1.3 where the numbers obtained on two fair dice ar...
 2.2.3.3: Consider again 2.1.4 where two cards are drawn from a pack of cards...
 2.2.3.4: ConsideragainthesalespersondiscussedinProblem2.1.9 who is trying to...
 2.2.3.5: Suppose that a player draws a card at random from a pack of cards, ...
 2.2.3.6: Two fair dice, one red and one blue, are rolled, and a fair coin is...
 2.2.3.7: A player pays $1 to play a game where three fair dice are rolled. I...
 2.2.3.8: A state lottery generally consists of many tickets being sold at pr...
 2.2.3.9: Suppose that you are organizing the game described at the end of Se...
 2.2.3.10: Consider again the random variable described in 2.2.2 with a probab...
 2.2.3.11: Consider again the random variable described in 2.2.4 with a cumula...
 2.2.3.12: Consider again the car panel painting machine discussed in 2.2.6. W...
 2.2.3.13: Consider again the plastic bending capabilities discussed in 2.2.8....
 2.2.3.14: Consider again the archery problem discussed in 2.2.9. What is the ...
 2.2.3.15: Prove that a continuous random variable with a probability density ...
 2.2.3.16: Recall 2.1.11 concerning the scheduling of appointments with a cons...
 2.2.3.17: Recall 2.2.11 concerning the resistance of an electrical component....
 2.2.3.18: A random variable has a probability density function f (x) = A(x 1....
 2.2.3.19: A manager notices that the number of items purchased by visitors to...
 2.2.4.1: Suppose that the random variable X takes the values2, 1, 4, and 6 w...
 2.2.4.2: Consider again the four copying machines discussed in 2.1.1 and 2.3...
 2.2.4.3: Consider again the salesperson discussed in 2.1.9 and 2.3.4 who is ...
 2.2.4.4: Suppose that you are organizing the game described at the end of Se...
 2.2.4.5: Consideragaintherandomvariabledescribedin 2.2.2 and 2.3.10 with a p...
 2.2.4.6: Consider again the random variable described in 2.2.4 and 2.3.11 wi...
 2.2.4.7: Consider again the car panel painting machine discussed in 2.2.6 an...
 2.2.4.8: Consider again the plastic bending capabilities discussed in 2.2.8 ...
 2.2.4.9: Consider again the archery problem discussed in 2.2.9 and 2.3.14. (...
 2.2.4.10: The time taken to serve a customer at a fastfood restaurant has a ...
 2.2.4.11: A machine produces iron bars whose lengths have a mean of 110.8 cm ...
 2.2.4.12: Recall 2.1.11 and 2.3.16 concerning the scheduling of appointments ...
 2.2.4.13: Recall 2.2.11 and 2.3.17 concerning the resistance of an electrical...
 2.2.4.14: A continuous random variable has a probability density function f (...
 2.2.4.15: In a game a player either loses $1 with a probability 0.25, wins $1...
 2.2.4.16: A random variable X has a probability density function f (x) = A/x ...
 2.2.4.17: When a construction project is opened for bidding, two proposals ar...
 2.2.4.18: A random variable X has a distribution given by the probability den...
 2.2.5.1: Consider Example 20 on mineral deposits. (a) Show that P(0.8 X 1,25...
 2.2.5.2: Consider Example 19 on air conditioner maintenance. (a) Suppose tha...
 2.2.5.3: Suppose that two continuous random variables X and Y have a joint p...
 2.2.5.4: A fair coin is tossed four times, and the random variable X is the ...
 2.2.5.5: Suppose that two continuous random variables X and Y have a joint p...
 2.2.5.6: Two cards are drawn without replacement from a pack of cards, and t...
 2.2.5.7: Repeat 2.5.6 when the second card is drawn with replacement.
 2.2.5.8: The random variable X measures the concentration of ethanol in a ch...
 2.2.5.9: Two safety inspectors inspect a new building and assign it a safety...
 2.2.5.10: Joint probability distributions of three or more random variables c...
 2.2.6.1: Suppose that the random variables X, Y, and Z are independent with ...
 2.2.6.2: Recall that for any function g(X) of a random variable X, E(g(X)) =...
 2.2.6.3: Suppose that X1, X2, and X3 are independent random variables each w...
 2.2.6.4: A machine part is assembled by fastening two components of type A a...
 2.2.6.5: In a game a player either wins $10 with a probability of 1/8 or los...
 2.2.6.6: The weight of a certain type of brick has an expectation of 1.12 kg...
 2.2.6.7: Ten cards are drawn with replacement from a pack of cards. What are...
 2.2.6.8: Suppose that the random variable X has a probability density functi...
 2.2.6.9: The radius of a soap bubble has a probability density function f (r...
 2.2.6.10: A rod of length L is bent until it snaps in two. The point of break...
 2.2.6.11: If$x isinvestedinmutualfundA,theannualreturnhasan expectation of $0...
 2.2.6.12: Recall 2.2.11, 2.3.17, and 2.4.13 concerning the resistance of an e...
 2.2.6.13: Suppose that items from a manufacturing process are subject to thre...
 2.2.6.14: The random variable X has an expectation of 77 and a standard devia...
 2.2.6.15: Suppose that components are manufactured such that their heights ar...
 2.2.6.16: An object has a weight W. When it is weighed with machine 1, a valu...
 2.2.6.17: A fair sixsided die is rolled 80 times and the sum of the 80 score...
 2.2.6.18: A relay race is run between team A and team B. Each team has four r...
 2.2.6.19: Suppose that a temperature has a mean of 110F and a standard deviat...
 2.2.6.20: A persons cholesterol level C can be measured by three different te...
 2.2.6.21: Suppose that the thicknesses of electrical components have a standa...
 2.2.6.22: Suppose that the impurity levels of water samples taken from a part...
 2.2.6.23: Suppose that the amount of money requested on a loan has a standard...
 2.2.6.24: Suppose that the amount of money requested on a loan has a standard...
 2.2.9.1: A box contains four red balls and two blue balls. Balls are drawn a...
 2.2.9.2: Theprobabilitymassfunctionofthenumberofcallstaken by a switchboard ...
 2.2.9.3: A box initially contains two red balls and two blue balls. At each ...
 2.2.9.4: Suppose that an ace, a king, a queen, and a jack are all worth 15 p...
 2.2.9.5: The acidity level X of a soil sample has a probability density func...
 2.2.9.6: Suppose that the random variables X and Y have a joint probability ...
 2.2.9.7: The density X of a chemical solution is f (x) = Ax + 2 x for 5 x 10...
 2.2.9.8: Recall that Var(aX+b) =a2Var(X) and Var(X1 + X2) =Var(X1)+Var(X1) i...
 2.2.9.9: Suppose that the scores from a test have a mean of 75 and a standar...
 2.2.9.10: If the random variables X and Y are related through the expression ...
 2.2.9.11: An insurance company charges a customer an annual premium of $100, ...
 2.2.9.12: Suppose that telephone calls on a particular line have an expected ...
 2.2.9.13: In an evaluation procedure, n items are ranked in order of effectiv...
 2.2.9.14: Nancy and Tom have to take a bus ride. The time taken by a bus for ...
 2.2.9.15: When a fair coin is tossed, 10 points are scored if a head is obtai...
 2.2.9.16: A continuous random variable has a probability density function f (...
 2.2.9.17: Components have a weight with an expectation of 438 and a standard ...
 2.2.9.18: In a game a player rolls a fair sixsided die. If the score is even...
 2.2.9.19: Are the following statements true or false? (a) The variance of a r...
 2.2.9.20: Suppose that the time taken to download a le of a certain kind onto...
 2.2.9.21: When a computer chip is examined to discover how many of the solder...
 2.2.9.22: A discrete random variable takes the values22, 3, 19, and 23 with p...
 2.2.9.23: A random variable has a probability density function f (x) = A/x2 f...
 2.2.9.24: Bricks have weights that have a mean 250 and a standard deviation 4...
 2.2.9.25: An evaluation score X1 of a candidate using method 1 has a mean of ...
 2.2.9.26: Wafers of type A have thicknesses with a mean of 134.9 and a standa...
 2.2.9.27: The standard deviation is a measure of the average value. A. True B...
 2.2.9.28: An investment in company I has an expected return of $150,000 and a...
Solutions for Chapter 2: Random Variables
Full solutions for Probability and Statistics for Engineers and Scientists  4th Edition
ISBN: 9781111827045
Solutions for Chapter 2: Random Variables
Get Full SolutionsProbability and Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9781111827045. This expansive textbook survival guide covers the following chapters and their solutions. Since 121 problems in chapter 2: Random Variables have been answered, more than 14251 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Probability and Statistics for Engineers and Scientists, edition: 4. Chapter 2: Random Variables includes 121 full stepbystep solutions.

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

`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).

Addition rule
A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).

Alternative hypothesis
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

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.

Categorical data
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.

Causal variable
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable

Chance cause
The portion of the variability in a set of observations that is due to only random forces and which cannot be traced to speciic sources, such as operators, materials, or equipment. Also called a common cause.

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
The probability of an event given that the random experiment produces an outcome in another event.

Conditional probability distribution
The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables

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

Continuous distribution
A probability distribution for a continuous random variable.

Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.

Defect
Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.

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

Dispersion
The amount of variability exhibited by data

Extra sum of squares method
A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.

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.

Gamma function
A function used in the probability density function of a gamma random variable that can be considered to extend factorials