a. Explanation Given info: Total number of orders selected at random is 15. There is about 20% of customers order an upgraded graphics card, 30% order an extra memory, 15% of customers order both upgraded graphics card and extra memory and 35% order neither. Calculation: The random variables X 1 , X 2 , X 3 , X 4 are defined as the number of orders in the four given categories. Then, X 1 , X 2 , X 3 , X 4 follows multinomial distribution with n = 15 , p 1 =0 .2 , p 2 =0 .3, p 3 =0 .15 and p 4 =0 .35 . Multinomial distribution: If the random variables X 1 , ... , X k follows multinomial distribution with parameters n , p 1 , p 2 , ... , p k , then the probability mass function of the random variables is, p ( x 1 , ... , x k ) = P ( X 1 = x 1 , ... , X k = x k ) = n ! x 1 ! x 2 ! ... x k ! p 1 x 1 p 2 x 2 ... p k x k x i = 0 , 1 , 2 , ... , n and ∑ x i = n Substitute n = 15 , p 1 =0 b. To determine Find the value of P ( X 1 = 3 ) .

4th Edition

ISBN: 9780073401331

Author: William Navidi Prof.

Publisher: McGraw-Hill Education

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Chapter 4.4, Problem 14E

To determine

Find the value of P(X1=3,X2=4,X3=2 and X4=6).

To determine

Find the value of P(X1=3).

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Chapter 4.4, Problem 13E

Chapter 4.4, Problem 15E

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Chapter 4 Solutions

Statistics for Engineers and Scientists

Ch. 4.1 - After scoring a touchdown, a football team may...Ch. 4.1 - A certain brand of dinnerware set comes in three...Ch. 4.1 - When a certain glaze is applied to a ceramic...Ch. 4.1 - Let X and Y be Bernoulli random variables. Let Z =...Ch. 4.1 - A penny and a nickel are tossed. Both are fair...Ch. 4.1 - Prob. 6E Ch. 4.1 - Prob. 7E Ch. 4.2 - Let X Bin(7, 0.3). Find a. P(X = 1) b. P(X = 2)...Ch. 4.2 - Let X Bin(9, 0.4). Find a. P(X 6) b. P(X 2) c....Ch. 4.2 - Prob. 3E

Ch. 4.2 - At a certain airport, 75% of the flights arrive on...Ch. 4.2 - Of all the registered automobiles in a certain...Ch. 4.2 - A fair die is rolled 8 times. a. What is the...Ch. 4.2 - Of all the weld failures in a certain assembly,...Ch. 4.2 - A general contracting firm experiences cost...Ch. 4.2 - Several million lottery tickets are sold, and 60%...Ch. 4.2 - A quality engineer takes a random sample of 100...Ch. 4.2 - In a random sample of 100 parts ordered from...Ch. 4.2 - Of the items manufactured by a certain process,...Ch. 4.2 - Of the bolts manufactured for a certain...Ch. 4.2 - Gears produced by a grinding process are...Ch. 4.2 - A commuter must pass through three traffic lights...Ch. 4.2 - A distributor receives a large shipment of...Ch. 4.2 - A k out of n system is one in which there is a...Ch. 4.2 - Refer to Exercise 17 for the definition of a k out...Ch. 4.2 - A certain large shipment comes with a guarantee...Ch. 4.2 - An insurance company offers a discount to...Ch. 4.2 - A message consists of a string of bits (0s and...Ch. 4.2 - Let X Bin(n, p), and let Y = n X. Show that Y ...Ch. 4.2 - Porcelain figurines are sold for 10 if flawless,...Ch. 4.2 - Prob. 24E Ch. 4.2 - (Requires material from Section 3.3.) Refer to...Ch. 4.2 - If p is a success probability, the quantity p/(1 ...Ch. 4.3 - Let X Poisson(4). Find a. P(X = 1) b. P(X = 0) c....Ch. 4.3 - The number of flaws in a given area of aluminum...Ch. 4.3 - In a certain city, the number of potholes on a...Ch. 4.3 - Geologists estimate the time since the most recent...Ch. 4.3 - Prob. 5E Ch. 4.3 - One out of every 5000 individuals in a population...Ch. 4.3 - The number of hits on a certain website follows a...Ch. 4.3 - The number of cars arriving at a given...Ch. 4.3 - Prob. 9E Ch. 4.3 - Prob. 10E Ch. 4.3 - A microbiologist wants to estimate the...Ch. 4.3 - Two-dimensional Poisson process. The number of...Ch. 4.3 - The number of defective components produced by a...Ch. 4.3 - The probability that a certain radioactive mass...Ch. 4.3 - The number of flaws in a certain type of lumber...Ch. 4.3 - Grandma is trying out a new recipe for raisin...Ch. 4.3 - Mom and Grandma are each baking chocolate chip...Ch. 4.3 - Prob. 18E Ch. 4.3 - Someone claims that a certain suspension contains...Ch. 4.3 - A physicist wants to estimate the rate of...Ch. 4.3 - Prob. 21E Ch. 4.4 - Twenty air-conditioning units have been brought in...Ch. 4.4 - There are 30 restaurants in a certain town. Assume...Ch. 4.4 - The probability that a computer running a certain...Ch. 4.4 - A traffic light at a certain intersection is green...Ch. 4.4 - Refer to Exercise 4. Let Y denote the number of...Ch. 4.4 - Refer to Exercise 4. What is the probability that...Ch. 4.4 - If X Geom(p), what is the most probable value of...Ch. 4.4 - A process that fills packages is stopped whenever...Ch. 4.4 - A system is tested for faults once per hour. If...Ch. 4.4 - Prob. 10E Ch. 4.4 - In a lot of 10 microcircuits, 3 are defective....Ch. 4.4 - A lot of parts contains 500 items, 100 of which...Ch. 4.4 - Ten items are to be sampled from a lot of 60. If...Ch. 4.4 - Prob. 14E Ch. 4.4 - Prob. 15E Ch. 4.4 - A thermocouple placed in a certain medium produces...Ch. 4.4 - Prob. 17E Ch. 4.4 - Prob. 18E Ch. 4.5 - Find the area under the normal curve a. To the...Ch. 4.5 - Find the area under the normal curve a. To the...Ch. 4.5 - Let Z N(0, 1). Find a constant c for which a. P(Z...Ch. 4.5 - If X N(2, 9), compute a. P(X 2) b. P(1 X 7) c....Ch. 4.5 - The lifetime of a battery in a certain application...Ch. 4.5 - The temperature recorded by a certain thermometer...Ch. 4.5 - Scores on a standardized test are approximately...Ch. 4.5 - Weights of female cats of a certain breed are...Ch. 4.5 - The lifetime of a lightbulb in a certain...Ch. 4.5 - In a certain university, math SAT scores for the...Ch. 4.5 - Penicillin is produced by the Penicillium fungus,...Ch. 4.5 - Specifications for an aircraft bolt require that...Ch. 4.5 - A cylindrical hole is drilled in a block, and a...Ch. 4.5 - Shafts manufactured for use in optical storage...Ch. 4.5 - The fill volume of cans filled by a certain...Ch. 4.5 - The amount of paint required to paint a surface...Ch. 4.5 - A fiber-spinning process currently produces a...Ch. 4.5 - The area covered by 1 L of a certain stain is...Ch. 4.5 - Prob. 19E Ch. 4.5 - The quality-assurance program for a certain...Ch. 4.5 - Two resistors, with resistances R1 and R2, are...Ch. 4.5 - The molarity of a solute in solution is defined to...Ch. 4.5 - A binary message m, where m is equal either to 0...Ch. 4.5 - Refer to Exercise 23. 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Find the MLE of p.Ch. 4.9 - Let X1, Xn be a random sample from a population...Ch. 4.9 - Maximum likelihood estimates possess the property...Ch. 4.9 - Let X1,, Xn be a random sample from a N(, 1)...Ch. 4.9 - Let X1, Xn be a random sample from a N(0,2)...Ch. 4.9 - Let X1,, Xn be a random sample from a N(,2)...Ch. 4.10 - Prob. 1E Ch. 4.10 - As part of a quality-control study aimed at...Ch. 4.10 - Below are the durations (in minutes) of 40...Ch. 4.10 - Prob. 4E Ch. 4.10 - Construct a normal probability plot for the PM...Ch. 4.10 - Construct a normal probability plot for the logs...Ch. 4.10 - Can the plot in Exercise 6 be used to determine...Ch. 4.10 - In the article Assessment of...Ch. 4.11 - Bottles filled by a certain machine are supposed...Ch. 4.11 - A 500-page book contains 250 sheets of paper. The...Ch. 4.11 - A commuter encounters four traffic lights each day...Ch. 4.11 - Among all the income-tax forms filed in a certain...Ch. 4.11 - Bags checked for a certain airline flight have a...Ch. 4.11 - The amount of warpage in a type of wafer used in...Ch. 4.11 - The time spent by a customer at a checkout counter...Ch. 4.11 - Drums labeled 30 L are filled with a solution from...Ch. 4.11 - The temperature of a solution will be estimated by...Ch. 4.11 - Among the adults in a large city, 30% have a...Ch. 4.11 - In a process that manufactures bearings, 90% of...Ch. 4.11 - A machine produces 1000 steel O-rings per day....Ch. 4.11 - Radioactive mass A emits particles at a mean rate...Ch. 4.11 - The concentration of particles in a suspension is...Ch. 4.11 - The concentration of particles in a suspension is...Ch. 4.11 - A battery manufacturer claims that the lifetime of...Ch. 4.11 - A new process has been designed to make ceramic...Ch. 4.11 - The manufacture of a certain part requires two...Ch. 4.11 - Seventy percent of rivets from vendor A meet a...Ch. 4.11 - Radiocarbon dating: Carbon-14 is a radioactive...Ch. 4 - An airplane has 100 seats for passengers. 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Let s 0 be an integer. a.Show...Ch. 4 - Prob. 26SE Ch. 4 - Prob. 27SE Ch. 4 - Prob. 28SE Ch. 4 - Prob. 29SE Ch. 4 - Prob. 30SE

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Find the value of P ( X 1 = 3 , X 2 = 4 , X 3 = 2 and X 4 = 6 ) .

Solution Summary: The author calculates that the probability mass function of the random variables is cp(x_1,mathrm...