Probability and Statistical Inference (9th Edition)
9th Edition
ISBN: 9780321923271
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
Publisher: PEARSON
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Chapter 2.5, Problem 4E
Suppose an airport metal detector catches a person with metal 99% of the time. That is. it misses detecting a person with metal 1 % of the time. Assume independence of people carrying metal. What is the
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Solve the following Probability Problem (solve all parts)
HW 2.x. (Headless Hunt)The Headless Hunt is an organization of 88 Hogwarts ghosts so elite thateven Nearly Headless Nick was annually denied admission for decades,despite being The Gryffindor ghost. The ghosts love playing sports anddecided to get together and have either a Head Polo tournament or aHorseback Head-Juggling tournament. However, even if they are ghosts,they still have jobs so some of them might have an urgent haunting as-signment. In order for no one to be left behind they need to be able tosplit into teams of equal numbers. Head polo teams consist of 4 playerswhereas Horseback Head-Juggling teams have 11 players. Assume thatany number of them from 1 to 88 show up with equal probability.
a) What is the probability they will be able to play one of the twotournaments?b) If in addition to the previous 2 sports there was one more option, atournament in Headless bowling which is played in teams of 8 players,what would…
42. Consider the following joint probability table.
B₁
B2
B3
B4
A
0.09
0.22
0.15
0.20
A
0.03
0.10
0.09
0.12
EXERCISES 4.3
Mechanics
41. Consider the following contingency table.
B
B
A
26
34
Ac
14
26
a. Convert the contingency table into a joint probability table.
b. What is the probability that A occurs?
ن فة
What is the probability that A and B occur?
d. Given that B has occurred, what is the probability that
A occurs?
e. Given that A has occurred, what is the probability that
B occurs?
f.
Are A and B mutually exclusive events? Explain.
g.
Are A and B independent events? Explain.
42. Consider the following joint probability table.
B₁
B2
B3
BA
A
0.09
0.22
0.15
0.20
Ac
0.03
0.10
0.09
0.12
Chapter 2 Solutions
Probability and Statistical Inference (9th Edition)
Ch. 2.1 - Let the pmf of X be defined by f(x)=x9,x=2,3,4.....Ch. 2.1 - Let a chip be taken at random from a bowl that...Ch. 2.1 - For each of the following, determine the constant...Ch. 2.1 - The state of Michigan generates a three-digit...Ch. 2.1 - The pmf of X is f(x)=(5x)10,x=1,2,3,4. (a) Graph...Ch. 2.1 - Let a random experiment consist of rolling a pair...Ch. 2.1 - Let a random experiment be the casting of a pair...Ch. 2.1 - A fair four-sided die has two faces numbered 0 and...Ch. 2.1 - Let the pmf of X be defined by...Ch. 2.1 - Prob. 10E
Ch. 2.1 - In a lot (collection) of 100 light bulbs, there...Ch. 2.1 - Let X be the number of accidents per week in a...Ch. 2.1 - A professor gave her students six essay questions...Ch. 2.1 - Often in buying a product at a supermarket, there...Ch. 2.1 - Five cards are selected at random without...Ch. 2.1 - Prob. 16ECh. 2.1 - A bag contains 144 ping-pong balls. More than half...Ch. 2.2 - Find E(X) for each of the distributions given in...Ch. 2.2 - Let the random variable X have the pmf...Ch. 2.2 - Let X be a discrete random variable with the...Ch. 2.2 - Prob. 4ECh. 2.2 - Let the random variable X be the number of days...Ch. 2.2 - Let the pmf of X be defined by...Ch. 2.2 - In Example 2.2-1 let Z=u(X)=X3. (a) Find the pmf...Ch. 2.2 - Let X be a random variable with support...Ch. 2.2 - In the gambling game chuck-a-luck, for a $1 bet it...Ch. 2.2 - In the casino game called high—low, there are...Ch. 2.2 - A roulette wheel used in an American casino has 38...Ch. 2.2 - Suppose that a school has 20 classes: 16 with 25...Ch. 2.3 - Find the mean, variance, and index of skewness for...Ch. 2.3 - For each of the following distributions, find...Ch. 2.3 - If the pmf of X is given by f(x), (I) depict the...Ch. 2.3 - Let and 2 denote the mean and variance of the...Ch. 2.3 - Consider an experiment that consists of selecting...Ch. 2.3 - Place eight chips in a bowl: Three have the number...Ch. 2.3 - Let X equal an integer selected at random from the...Ch. 2.3 - Let X equal the larger outcome when two fair...Ch. 2.3 - A warranty is written on a product worth $10,000...Ch. 2.3 - Let X be a discrete random variable with pmf...Ch. 2.3 - If the moment-generating function of X is...Ch. 2.3 - Let X equal the number of people selected at...Ch. 2.3 - For each question on a multiple-choice test, there...Ch. 2.3 - The probability that a machine produces a...Ch. 2.3 - Apples are packaged automatically in 3-pound bags....Ch. 2.3 - Let X equal the number of flips of a fair coin...Ch. 2.3 - Let X equal the number of flips of a fair coin...Ch. 2.3 - Let X have a geometric distribution. Show that...Ch. 2.3 - Given a random permutation of the integers in the...Ch. 2.4 - An urn contains seven red and 11 white balls. Draw...Ch. 2.4 - Suppose that in Exercise 2.4-1, X = 1 if a red...Ch. 2.4 - On a six-question multiple-choice test there are...Ch. 2.4 - It is claimed that 15% of the ducks in a...Ch. 2.4 - In a lab experiment involving inorganic syntheses...Ch. 2.4 - It is believed that approximately 75% of American...Ch. 2.4 - Suppose that 2000 points are selected...Ch. 2.4 - A boiler has four relief valves. The probability...Ch. 2.4 - Suppose that the percentage of American drivers...Ch. 2.4 - A certain type of mint has a label weight of 20.4...Ch. 2.4 - Find the index of skewness for the b(n,p)...Ch. 2.4 - In the casino game chuck-a-luck, three fair six-...Ch. 2.4 - It is claimed that for a particular lottery, 110...Ch. 2.4 - For the lottery described in Exercise 2.4-13, find...Ch. 2.4 - A hospital obtains 40% of its flu vaccine from...Ch. 2.4 - A company starts a fund of M dollars from which it...Ch. 2.4 - Your stockbroker is free to take your calls about...Ch. 2.4 - In group testing for a certain disease, a blood...Ch. 2.4 - Define the pmf and give the values of ,2, and ...Ch. 2.4 - Prob. 20ECh. 2.5 - An excellent free-throw shooter attempts several...Ch. 2.5 - Show that 63512 is the probability that the fifth...Ch. 2.5 - Suppose that a basketball player different from...Ch. 2.5 - Suppose an airport metal detector catches a person...Ch. 2.5 - Let the moment-generating function M(t) of X exist...Ch. 2.5 - Use the result of Exercise 2.6-5 to find the mean...Ch. 2.5 - If E(Xr)=5r,r=1,2,3.... find the moment-generating...Ch. 2.5 - The probability that a companys workforce has no...Ch. 2.5 - One of four different prizes was randomly put into...Ch. 2.5 - In 2016, Red Rose tea randomly began placing one...Ch. 2.6 - Let X have a Poisson distribution with a mean of...Ch. 2.6 - Let X have a Poisson distribution with a variance...Ch. 2.6 - Customers arrive at a travel agency at a mean rate...Ch. 2.6 - If X has a Poisson distribution such that...Ch. 2.6 - Flaws in a certain type of drapery material appear...Ch. 2.6 - Find the index of skewness of a Poisson...Ch. 2.6 - With probability 0.001, a prize of $499 is won in...Ch. 2.6 - Suppose that the probability of suffering a side...Ch. 2.6 - A store selling newspapers orders only n = 4 of a...Ch. 2.6 - The mean of a Poisson random variable X is =9....Ch. 2.6 - An airline always overbooks if possible. A...Ch. 2.6 - A baseball team loses $100,000 for each...Ch. 2.6 - Assume that a policyholder is four times more...
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