PROB SOLV APPROACH FOR TEACHERS MYLAB
12th Edition
ISBN: 9780137657988
Author: BILLSTEIN
Publisher: INTER PEAR
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Chapter 9.3B, Problem 14A
To determine
To find:
The probability of the event of winning the lottery.
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5. Let X be a positive random variable with finite variance, and let A = (0, 1).
Prove that
P(X AEX) 2 (1-A)² (EX)²
EX2
6. Let, for p = (0, 1), and xe R. X be a random variable defined as follows:
P(X=-x) = P(X = x)=p. P(X=0)= 1-2p.
Show that there is equality in Chebyshev's inequality for X.
This means that Chebyshev's inequality, in spite of being rather crude, cannot be
improved without additional assumptions.
4. Prove that, for any random variable X, the minimum of EIX-al is attained for
a = med (X).
Chapter 9 Solutions
PROB SOLV APPROACH FOR TEACHERS MYLAB
Ch. 9.1 - Explain whether you think that when dialling a...Ch. 9.1 - Prob. 2MCCh. 9.1 - Prob. 3MCCh. 9.1 - Prob. 4MCCh. 9.1 - Prob. 5MCCh. 9.1 - Prob. 8MCCh. 9.1 - If possible, for each of the following letters,...Ch. 9.1 - Prob. 13MCCh. 9.1 - A student observes the following spinner and...Ch. 9.1 - Prob. 15MC
Ch. 9.1 - Prob. 16MCCh. 9.1 - Prob. 17MCCh. 9.1 - Joe claims that if the following spinner is spun...Ch. 9.1 - Suppose the figure in exercise 14 is a is a...Ch. 9.1 - Prob. 20MCCh. 9.1 - Mark has nine shirts in his closet as shown. If...Ch. 9.1 - Ms. Livingstons class spins the arrow on the...Ch. 9.1 - Prob. 3NAEPCh. 9.1 - A bag contains two red candies and one yellow...Ch. 9.1A - Consider the experiment of drawing a single card...Ch. 9.1A - Is it likely that a number drawn from the first...Ch. 9.1A - Each letter of the alphabet is written on a...Ch. 9.1A - The spinner shown is spun. Find the probability of...Ch. 9.1A - A card is selected from a ordinary deck of 52...Ch. 9.1A - Prob. 6ACh. 9.1A - Riena has six unmarked files on her computer, one...Ch. 9.1A - According to a weather report, there is a 30...Ch. 9.1A - A set of dolls is in a packing crate: 17 with...Ch. 9.1A - The plays generally considered the tragedies by...Ch. 9.1A - In the childrens song Old MacDonald Had a Farm,...Ch. 9.1A - Prob. 12ACh. 9.1A - If A and B are mutually exclusive, P(A)=0.3, and...Ch. 9.1A - A calculus class is composed of 35 men and 45...Ch. 9.1A - A box contains five white balls, three black balls...Ch. 9.1A - Zoe is playing a game in which she draws one ball...Ch. 9.1A - If you flipped a fair coin 15 times and got 15...Ch. 9.1A - Prob. 18ACh. 9.1A - A witness identified all the digits on a license...Ch. 9.1A - Prob. 20ACh. 9.1A - The experimental probability of rolling a 4 on a...Ch. 9.1A - How many times would you except to obtain a 4 on a...Ch. 9.1B - Prob. 1ACh. 9.1B - An experiment consists of selecting the rightmost...Ch. 9.1B - The name of a member of the U.S. Congress is drawn...Ch. 9.1B - Prob. 4ACh. 9.1B - Prob. 5ACh. 9.1B - Prob. 6ACh. 9.1B - Prob. 7ACh. 9.1B - In each of the following scenarios, sketch a...Ch. 9.1B - Prob. 9ACh. 9.1B - Prob. 10ACh. 9.1B - Prob. 11ACh. 9.1B - Prob. 12ACh. 9.1B - Prob. 13ACh. 9.1B - Prob. 14ACh. 9.1B - Prob. 15ACh. 9.1B - Prob. 16ACh. 9.1B - Prob. 17ACh. 9.1B - What is the probability of choosing a continent at...Ch. 9.1B - Prob. 20ACh. 9.1B - Prob. 21ACh. 9.1B - How many times would you except to obtain a 6 on a...Ch. 9.2 - Jim rolled a fair die 5 times and obtained a 3...Ch. 9.2 - A witness to a crime observed that the criminal...Ch. 9.2 - You are given three white balls, one red ball, and...Ch. 9.2 - Prob. 4MCCh. 9.2 - Could the probability of two independent events...Ch. 9.2 - Make up a game in which the players have an equal...Ch. 9.2 - How can the faces of two cubes be numbered so that...Ch. 9.2 - Mathematical Connections Design a pair of...Ch. 9.2 - An experiment consists of tossing a fair coin...Ch. 9.2 - A student would like to know the difference...Ch. 9.2 - In response to the question, If a fair die is...Ch. 9.2 - A student is not sure when to add and when to...Ch. 9.2 - Alberto is to spin the spinners shown and compute...Ch. 9.2 - Prob. 20MCCh. 9.2 - Match the following phrase to the probability that...Ch. 9.2 - A date in the month of April is chosen at random....Ch. 9.2 - Three men were walking down a street talking when...Ch. 9.2 - A roulette wheel has 38 slots around the rim; 36...Ch. 9.2 - Prob. 25MCCh. 9.2 - Prob. 1NAEPCh. 9.2 - Prob. 2NAEPCh. 9.2A - Assessment a. A box contains three white balls and...Ch. 9.2A - Prob. 2ACh. 9.2A - An executive committee consisted of 10 members: 4...Ch. 9.2A - Following are three boxes containing balls. Draw a...Ch. 9.2A - Assume the probability is 12 that a child born at...Ch. 9.2A - Prob. 6ACh. 9.2A - In a game, there are one black marble and one...Ch. 9.2A - Prob. 8ACh. 9.2A - If a person takes a five-question true-false test,...Ch. 9.2A - Assessment Rattlesnake and Paxson Colleges play...Ch. 9.2A - Consider the following dartboard where all...Ch. 9.2A - Prob. 12ACh. 9.2A - There are 40 employees in a certain firm. We know...Ch. 9.2A - Prob. 14ACh. 9.2A - When you toss a quarter 4 times, what is the...Ch. 9.2A - Prob. 16ACh. 9.2A - Bob leaves the top of Snow Mountain for his last...Ch. 9.2A - Carolyn wins a large prize if she wins two tennis...Ch. 9.2A - A bag contain 3 blue marbles, 4 red marbles, and 3...Ch. 9.2A - Prob. 20ACh. 9.2A - Prob. 21ACh. 9.2A - Prob. 22ACh. 9.2B - Suppose an experiment consists of spinning X and...Ch. 9.2B - Prob. 2ACh. 9.2B - A penny, a nickel, a dime, and a quarter are...Ch. 9.2B - Prob. 4ACh. 9.2B - An assembly line has two inspectors. The...Ch. 9.2B - Prob. 6ACh. 9.2B - Prob. 9ACh. 9.2B - Prob. 11ACh. 9.2B - Prob. 13ACh. 9.2B - Prob. 14ACh. 9.2B - A husband and wife discover that there is a 10...Ch. 9.2B - Prob. 16ACh. 9.2B - Prob. 18ACh. 9.2B - Prob. 21ACh. 9.2B - Prob. 22ACh. 9.3 - Prob. 1MCCh. 9.3 - Prob. 2MCCh. 9.3 - A game involves tossing two coins. A player wins...Ch. 9.3 - Prob. 4MCCh. 9.3 - Suppose we toss two fair coins. Design a fair game...Ch. 9.3 - Prob. 8MCCh. 9.3 - Prob. 9MCCh. 9.3 - Prob. 16MCCh. 9.3 - Prob. 17MCCh. 9.3 - Prob. 18MCCh. 9.3 - Prob. 19MCCh. 9.3 - Prob. 20MCCh. 9.3 - Prob. 21MCCh. 9.3 - From a sack containing seven red marbles, eight...Ch. 9.3 - Prob. 23MCCh. 9.3 - Prob. 24MCCh. 9.3 - Prob. 25MCCh. 9.3 - Prob. 26MCCh. 9.3A - Could we use a thumb tack to simulate the birth of...Ch. 9.3A - Prob. 2ACh. 9.3A - Prob. 4ACh. 9.3A - Prob. 5ACh. 9.3A - Prob. 6ACh. 9.3A - Pick a block of two digits from the random-digit...Ch. 9.3A - Prob. 8ACh. 9.3A - Prob. 10ACh. 9.3A - a. What are the odds in favor of drawing a face...Ch. 9.3A - Prob. 12ACh. 9.3A - If the probability of a boys being born is 12, and...Ch. 9.3A - If the odds against Deborahs winning first prize...Ch. 9.3A - If the probability of the event that a randomly...Ch. 9.3A - From a set of eight marbles, five red and three...Ch. 9.3A - In exercise 16, what are the odds against choosing...Ch. 9.3A - Prob. 18ACh. 9.3A - Prob. 19ACh. 9.3A - Prob. 20ACh. 9.3A - Prob. 21ACh. 9.3A - What are the odds in favor of rolling double sixes...Ch. 9.3A - Suppose five quarters, five dimes, fives nickels,...Ch. 9.3A - If the odds in favor of Fast Leg winning a horse...Ch. 9.3A - Prob. 25ACh. 9.3A - Prob. 26ACh. 9.3A - Prob. 27ACh. 9.3A - Assessment If the probability of spilling soup on...Ch. 9.3A - Assessment A bag of grass seed is advertised as...Ch. 9.3A - Prob. 30ACh. 9.3B - How could we use a spinner as shown below to...Ch. 9.3B - How could we use a random-digit generator or...Ch. 9.3B - Prob. 3ACh. 9.3B - Prob. 4ACh. 9.3B - Prob. 5ACh. 9.3B - Use a random-number table to estimate the...Ch. 9.3B - Prob. 10ACh. 9.3B - a. Susan said that the odds in favor of drawing a...Ch. 9.3B - Prob. 12ACh. 9.3B - Prob. 13ACh. 9.3B - Prob. 14ACh. 9.3B - Prob. 15ACh. 9.3B - Prob. 16ACh. 9.3B - Prob. 17ACh. 9.3B - Prob. 18ACh. 9.3B - Prob. 19ACh. 9.3B - Prob. 20ACh. 9.3B - Prob. 21ACh. 9.3B - On a roulette wheel, half of the slots numbered 1...Ch. 9.3B - Prob. 24ACh. 9.3B - Suppose a standard six-sided die is rolled and you...Ch. 9.3B - Prob. 26ACh. 9.3B - Prob. 27ACh. 9.3B - Prob. 28ACh. 9.3B - Prob. 29ACh. 9.3B - Prob. 30ACh. 9.4 - The terms Fundamental Counting Principle,...Ch. 9.4 - A bicycle lock has three reels, each of which...Ch. 9.4 - In how many ways can five couples be seated in a...Ch. 9.4 - Prob. 5MCCh. 9.4 - Prob. 6MCCh. 9.4 - Prob. 7MCCh. 9.4 - Prob. 8MCCh. 9.4 - Prob. 9MCCh. 9.4 - A student does not understand the meaning of 4P0 ....Ch. 9.4 - Prob. 11MCCh. 9.4 - Prob. 12MCCh. 9.4 - Prob. 13MCCh. 9.4 - If two regular dice are tossed, what is...Ch. 9.4 - On a roulette wheel, the probability of the event...Ch. 9.4 - Prob. 1NAEPCh. 9.4 - Prob. 2NAEPCh. 9.4A - The eighth grade class at a grade school has 16...Ch. 9.4A - Prob. 2ACh. 9.4A - Carlins Pizza House offer 3 kinds of salad, 15...Ch. 9.4A - Prob. 4ACh. 9.4A - Find the number of ways to arrange the letter in...Ch. 9.4A - Prob. 6ACh. 9.4A - Assume a class has 30 members a. In how many ways...Ch. 9.4A - A five-volume numbered set of books is placed...Ch. 9.4A - There are 10 points in a plane, no 3 of them on a...Ch. 9.4A - Prob. 10ACh. 9.4A - At a party, 28 handshakes took place. Each person...Ch. 9.4A - Prob. 12ACh. 9.4A - In a certain lottery game, 54 numbers are randomly...Ch. 9.4A - From a group of 10 boys and 12 girls, a committee...Ch. 9.4A - From a group 20 Britons, 21 Italians, and 4 Danes,...Ch. 9.4A - Prob. 16ACh. 9.4A - A company is setting up four-digit ID numbers for...Ch. 9.4A - Prob. 18ACh. 9.4A - Your English teacher asks that you read any three...Ch. 9.4A - Prob. 20ACh. 9.4A - Prob. 21ACh. 9.4A - Prob. 22ACh. 9.4B - Prob. 1ACh. 9.4B - Assessment Radio stations in the United States...Ch. 9.4B - Prob. 4ACh. 9.4B - Find the number of ways to arrange the letters in...Ch. 9.4B - Prob. 6ACh. 9.4B - Prob. 7ACh. 9.4B - Prob. 8ACh. 9.4B - Prob. 9ACh. 9.4B - Prob. 10ACh. 9.4B - How many different 12-person juries can be...Ch. 9.4B - Prob. 12ACh. 9.4B - Prob. 13ACh. 9.4B - A committee of three people is selected at random...Ch. 9.4B - A club selects an executive committee of 5 and...Ch. 9.4B - Assume the probability of the event of a...Ch. 9.4B - Prob. 18ACh. 9.4B - Prob. 19ACh. 9.4B - Prob. 20ACh. 9.4B - How many arrangements can be made from the letters...Ch. 9.4B - In how many ways can a group of 9 people stand in...Ch. 9.CR - Prob. 1CRCh. 9.CR - Prob. 2CRCh. 9.CR - Prob. 3CRCh. 9.CR - In the 2012 election, Barack Obama received 65,...Ch. 9.CR - Prob. 5CRCh. 9.CR - Prob. 6CRCh. 9.CR - Prob. 7CRCh. 9.CR - Prob. 8CRCh. 9.CR - Prob. 9CRCh. 9.CR - Prob. 10CRCh. 9.CR - Prob. 11CRCh. 9.CR - Prob. 12CRCh. 9.CR - Prob. 13CRCh. 9.CR - A game consists of rolling two dice. Rolling...Ch. 9.CR - Prob. 15CRCh. 9.CR - Prob. 16CRCh. 9.CR - Prob. 17CRCh. 9.CR - Prob. 18CRCh. 9.CR - Prob. 19CRCh. 9.CR - Prob. 20CRCh. 9.CR - Prob. 21CRCh. 9.CR - Prob. 22CRCh. 9.CR - Prob. 23CRCh. 9.CR - Prob. 24CRCh. 9.CR - Prob. 25CRCh. 9.CR - Prob. 26CRCh. 9.CR - Prob. 28CRCh. 9.CR - Prob. 29CRCh. 9.CR - Prob. 30CRCh. 9.CR - Prob. 31CRCh. 9.CR - Prob. 32CRCh. 9.CR - Prob. 33CRCh. 9.CR - Prob. 34CRCh. 9.CR - Prob. 35CRCh. 9.CR - Prob. 36CRCh. 9.CR - Prob. 37CRCh. 9 - NOW TRY THIS a. In an experiment of tossing a fair...Ch. 9 - In the following cartoon, assume that the events...Ch. 9 - Prob. 5NTCh. 9 - Prob. 6NTCh. 9 - Prob. 7NTCh. 9 - Prob. 8NT
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