Probability And Statistical Inference (10th Edition)
10th Edition
ISBN: 9780135189399
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
Publisher: PEARSON
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Chapter 2.3, Problem 14E
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Pam, Ron, and Sam are using the method of sealed bids to divide among themselves four items. Table on the next page shows the bids that each player makes for each item. Use this example to answer questions 19 to 23
Pam
Ron
Sam
Bedroom Set
$860
$550
$370
Dining Room Set
$350
$420
$500
Television
$230
$440
$340
Sofa set
$480
$270
$230
What is the value of Sam’s fair share
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None of these
$360
$370
$500
$480
In a survey, the planning value for the population proportion is p 0.25. How large a sample should be taken to provide a 95% confidence interval with a margin of error
of 0.03? Round your answer up to the next whole number.
800
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Chapter 2 Solutions
Probability And Statistical Inference (10th 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 - Let X be a discrete random variable with pmf...Ch. 2.1 - The pmf of X is f(x)=(5x)10,x=1,2,3,4. (a) Graph...Ch. 2.1 - The state of Michigan generates a three-digit...Ch. 2.1 - Let a random experiment be the casting of a pair...Ch. 2.1 - Let a random experiment consist of rolling a pair...Ch. 2.1 - Let the pmf of X be defined by...Ch. 2.1 - A fair four-sided die has two faces numbered 0 and...
Ch. 2.1 - Let X be the number of accidents per week in a...Ch. 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. 2.2 - In the gambling game craps (see Exercise 1.3-13),...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. 2.3 - Construct a sequence of squares in the first...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 - In a lot (collection) of 100 light bulbs, there...Ch. 2.5 - On Wednesday afternoons, eight men play tennis on...Ch. 2.5 - A professor gave her students six essay questions...Ch. 2.5 - When a customer buys a product at a supermarket,...Ch. 2.5 - Five cards are selected at random without...Ch. 2.5 - To find the variance of a hyper geometric random...Ch. 2.5 - In the Michigan lottery game, LOT 10 47, the state...Ch. 2.5 - Forty-four states. Washington D.C., and the Virgin...Ch. 2.5 - Suppose there are three defective items in a lot...Ch. 2.5 - Prob. 10ECh. 2.5 - A Bingo card has 25 squares with numbers on 24 of...Ch. 2.6 - An excellent free-throw shooter attempts several...Ch. 2.6 - Show that 63512 is the probability that the fifth...Ch. 2.6 - Suppose that a basketball player different from...Ch. 2.6 - Suppose an airport metal detector catches a person...Ch. 2.6 - Let the moment-generating function M(t) of X exist...Ch. 2.6 - Use the result of Exercise 2.6-5 to find the mean...Ch. 2.6 - If E(Xr)=5r,r=1,2,3.... find the moment-generating...Ch. 2.6 - The probability that a companys workforce has no...Ch. 2.6 - One of four different prizes was randomly put into...Ch. 2.6 - In 2016, Red Rose tea randomly began placing one...Ch. 2.7 - Let X have a Poisson distribution with a mean of...Ch. 2.7 - Let X have a Poisson distribution with a variance...Ch. 2.7 - Customers arrive at a travel agency at a mean rate...Ch. 2.7 - If X has a Poisson distribution such that...Ch. 2.7 - Flaws in a certain type of drapery material appear...Ch. 2.7 - Find the index of skewness of a Poisson...Ch. 2.7 - With probability 0.001, a prize of $499 is won in...Ch. 2.7 - Suppose that the probability of suffering a side...Ch. 2.7 - A store selling newspapers orders only n = 4 of a...Ch. 2.7 - The mean of a Poisson random variable X is =9....Ch. 2.7 - An airline always overbooks if possible. A...Ch. 2.7 - A baseball team loses $100,000 for each...Ch. 2.7 - Assume that a policyholder is four times more...
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- Find the LaPla se trnsofrom of a) chi-square Distribution. b) Normal Distribution. C) Gamma Distribution. prove that Binomial (n, 2) Poisson (2) *********************arrow_forward-xx0. B2 If Xfx(x) find the MGF in the case that fx(x) = - 1 28 exp{-|x − a\/ẞ}, Use the MGF to compute E(X) and Var(X).arrow_forwardB3 Consider X ~ Bern(p) (a) Find Mx(t), the moment generating function of X. iid (b) If X1,..., Xn Bern(p), find the MGF, say My (t) of n Y = ΣΧ (c) Using the fact that i=1 n lim (1 (1+2)"= N→X = e² find limn→∞ My (t) in the case that p satisfies limn→∞ np = λ, say. (d) State the distribution of Y in the case that n is not large, and the distribution of Y in the limiting case described in the question.arrow_forward
- B1 The density of the x2 distribution is given in the notes as 1 F(§)2/2 (x)=()2/21 x/2-1/2, if x > 0, and e where I(t)=√xt-¹e dx is the gamma function. otherwise, Find the point at which o(a) has its maximum, i.e. find arg max, o, (x)arrow_forward18. Let X be normally distributed with mean μ = 2,500 and stan- dard deviation σ = 800. a. Find x such that P(X ≤ x) = 0.9382. b. Find x such that P(X>x) = 0.025. ة نفـة C. Find x such that P(2500arrow_forward17. Let X be normally distributed with mean μ = 2.5 and standard deviation σ = 2. a. Find P(X> 7.6). b. Find P(7.4≤x≤ 10.6). 21 C. Find x such that P(X>x) = 0.025. d. Find x such that P(X ≤x≤2.5)= 0.4943. and stan-arrow_forward
- 16. Let X be normally distributed with mean μ = 120 and standard deviation σ = 20. a. Find P(X86). b. Find P(80 ≤x≤ 100). ة ن فـ d. Find x such that P(X ≤x) = 0.40. Find x such that P(X>x) = 0.90.arrow_forwardhe following contingency table details the sex and age distribution of the patients currently registered at a family physician's medical practice. If the doctor sees 17 patients per day, use the binomial formula and the information contained in the table to answer the question: SEX AGE Under 20 20-39 40-59 60-79 80 or over TOTAL Male 5.6% 12.8% 18.4% 14.4% 3.6% 54.8% Female 2.8% 9.6% 13.2% 10.4% 9.2% 45.2% TOTAL 8.4% 22.4% 31.6% 24.8% 12.8% 100.0% if the doctor sees 6 male patients in a day, what is the probability that at most half of them are aged under 39?arrow_forwardPam, Rob and Sam get a cake that is one-third chocolate, one-third vanilla, and one-third strawberry as shown below. They wish to fairly divide the cake using the lone chooser method. Pam likes strawberry twice as much as chocolate or vanilla. Rob only likes chocolate. Sam, the chooser, likes vanilla and strawberry twice as much as chocolate. In the first division, Pam cuts the strawberry piece off and lets Rob choose his favorite piece. Based on that, Rob chooses the chocolate and vanilla parts. Note: All cuts made to the cake shown below are vertical.What pieces would Sam choose based on the Pam and Rob's second division of their own pieces?arrow_forward
- Please plot graphs to represent the functionsarrow_forwardEXAMPLE 6.2 In Example 5.4, we considered the random variables Y₁ (the proportional amount of gasoline stocked at the beginning of a week) and Y2 (the proportional amount of gasoline sold during the week). The joint density function of Y₁ and Y2 is given by 3y1, 0 ≤ y2 yı≤ 1, f(y1, y2) = 0, elsewhere. Find the probability density function for U = Y₁ - Y₂, the proportional amount of gasoline remaining at the end of the week. Use the density function of U to find E(U).arrow_forward7.20 a If U has a x² distribution with v df, find E(U) and V (U). b Using the results of Theorem 7.3, find E(S2) and V (S2) when Y₁, Y2,..., Y, is a random sample from a normal distribution with mean μ and variance o².arrow_forward
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