Introductory Statistics
1st Edition
ISBN: 9781938168208
Author: Barbara Illowsky, Susan Dean
Publisher: OpenStax College
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Textbook Question
Chapter 5, Problem 6P
For a continuous probablity distribution,
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3. Let X Pois(4). Find the distribution of Y = √X.
Suppose that you enter a fantasy basketball league. Suppose that the 2022
team budget, say X, is randomly drawn from a uniform distribution on
the interval [90, 210], where the unit is U.S. million dollars. In addition,
suppose that after the value X = x has been observed (90 < x < 210), the
2023 team budget, say Y, is randomly drawn from a uniform distribution
on the interval [x, 210]. In other words, the 2023 budget is at least as large
as the 2022 budget.
(a) For any given value of x (90 < x < 210), obtain E[Y|X = x].
(b) In view of part (i), obtain E[Y|X].
(c) What is the difference between E[Y|X = x] and E[Y|X]?
(d) Obtain E[Y]. That is, what is the expected value of your 2023 fantasy
basketball budget?
(e) Golden State Warriors won the 2022 NBA finals. Their estimated
2022 payroll is about $194 million. Would your 2023 fantasy basketball
budget be on average larger than Golden State Warriors' 2022 payroll?
Explain briefly.
For a highway, the car's speed has a uniform distribution [50,90]. Cars are stopped if speed X is greater than 70(mph). The price of a speeding ticket is equal to Y = 15 + (1/10)X(X-70).
What is the probability that a stopped car is/was going faster than 85 mph?
For each car stopped, the Var(X) is equal to what?
Chapter 5 Solutions
Introductory Statistics
Ch. 5 - Consider the function f(x)=18 for 0x8 0. Draw the...Ch. 5 - The data the follow are the number of passengers...Ch. 5 - A distribution is given as X ~U(0, 20). What is...Ch. 5 - The total duration of baseball games in the major...Ch. 5 - Suppose the time it takes a student to finish a...Ch. 5 - The amount of time a service technician needs to...Ch. 5 - The amount of time spouses shop for anniversary...Ch. 5 - The number of days ahead travelers purchase their...Ch. 5 - On average, a pair of running shoes can last 18...Ch. 5 - Suppose that the distance, in miles, that people...
Ch. 5 - Suppose that on a certain stretch of highway, cars...Ch. 5 - Suppose that the longevity of a light bulb is...Ch. 5 - In a small city the number of automobile accidents...Ch. 5 - Which type of distribution does the graph...Ch. 5 - Which type of distribution does the graph...Ch. 5 - Which type of distribution does the graph...Ch. 5 - What does the shaded area represent? P(_< x <_)...Ch. 5 - What does the shaded area represent? P(______...Ch. 5 - For a continuous probablity distribution, 0x15 ....Ch. 5 - What is the area under f(x) if the function is a...Ch. 5 - For a continuous probability distribution, 0x10 ....Ch. 5 - A continuous probability function is restricted to...Ch. 5 - f(x) for a continuous probability function is 15 ,...Ch. 5 - f(x) , a continuous probability function, is equal...Ch. 5 - Find the probability that x falls in the shaded...Ch. 5 - Find the probability that x falls in the shaded...Ch. 5 - Find the probability that x falls in the shaded...Ch. 5 - m:math display='block'>f(x), a continuous...Ch. 5 - Use the following information to answer the next...Ch. 5 - Use the following information to answer the next...Ch. 5 - Use the following information to answer the next...Ch. 5 - Use the following information to answer the next...Ch. 5 - Use the following information to answer the next...Ch. 5 - Use the following information to answer the next...Ch. 5 - the following information to answer the next ten...Ch. 5 - 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Use the following information to answer the next...Ch. 5 - Use the following information to answer the next...Ch. 5 - Use the following information to answer the next...Ch. 5 - Use the following information to answer the next...Ch. 5 - Use the following information to answer the next...Ch. 5 - Use the following information to answer the next...Ch. 5 - Use the following information to answer the next...Ch. 5 - Use the following information to answer the next...Ch. 5 - Use the following information to answer the next...Ch. 5 - Use the following information to answer the next...Ch. 5 - Use the following information to answer the next...Ch. 5 - Use the following information to answer the next...Ch. 5 - Use the following information to answer the net 16...Ch. 5 - Use the following information to answer the net 16...Ch. 5 - Use the following information to answer the net 16...Ch. 5 - For each probability and percentile problem, draw...Ch. 5 - For each probability and percentile problem, draw...Ch. 5 - For each probability and percentile problem, draw...Ch. 5 - For each probability and percentile problem, draw...Ch. 5 - For each probability and percentile problem, draw...Ch. 5 - For each probability and percentile problem, draw...Ch. 5 - For each probability and percentile problem, draw...Ch. 5 - Use the following information o answer the next...Ch. 5 - Use the following information o answer the next...Ch. 5 - Use the following information o answer the next...Ch. 5 - The time (In minutes) until the next bus departs a...Ch. 5 - Suppose that the value of a stock varies each day...Ch. 5 - A fireworks show is designed so that the time...Ch. 5 - The number of miles driven by a truck driver falls...Ch. 5 - Suppose that the length of long distance phone...Ch. 5 - Suppose that the useful life of a particular car...Ch. 5 - The percent of persons (ages five and older) in...Ch. 5 - The time (In years) after reaching age 60 that ft...Ch. 5 - The cost of all maintenance for a car during fts...Ch. 5 - Use the following information to answer the next...Ch. 5 - Use the following information to answer the next...Ch. 5 - Use the following information to answer the next...Ch. 5 - Let X ~ Exp(0.l). a. decay rate = _________ b. ...Ch. 5 - Suppose that the longevity of a light bulb is...Ch. 5 - At a 911 call center, calls come in a an average...Ch. 5 - In major league baseball, a no-hitter is a game in...Ch. 5 - During the years 1998—2012. a total of 29...Ch. 5 - According to the American Red Cross. about one out...Ch. 5 - A web site experiences traffic during normal...Ch. 5 - At an urgent care faci11t; patients arrive at an...
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- Assume that the probability that an airplane engine will fail during a torture test is 12and that the aircraft in question has 4 engines. Construct a sample space for the torture test. Use S for survive and F for fail.arrow_forwardIf a binomial experiment has probability p success, then the probability of failure is ____________________. The probability of getting exactly r successes in n trials of this experiment is C(_________, _________)p (1p)arrow_forwardThe median of the distribution X having p. d. f. S3x²,0arrow_forwardLet. X have a uniform distribution on the interval (1,3). What is the proba- bility that the sum of 2 independent observations of X is greater than 5?arrow_forwardAssume y follows theX distribution. Assume c₁ and c₂ satisfy P(Y> c₁) = 0.05 and P(Y < c₂) (b). = 0.05. Then C₁ = (a) and C2 =arrow_forward1Example 23. A distribution x1, X2,..., Xp., Xp with frequencies, fp f2,..., f..., fn is transformed into the distribution y1, y2,.….., Y,.., yn with the same corresponding frequencies by the relation y, = ax, + b, where a and b are constants. Show that the mean, median and mode of the new distribution are given in terms of the first distribution by the same transformation.arrow_forwardAt a particular fast-food restaurant, food is often made in advance, and then it is placed under a heater until it is sold. The distribution function for the number of minutes that passes between when a cheeseburger is made and when it is sold is given by f(t) = { 17-23³t if 0≤t≤17 289 otherwise. Find the median number of minutes that a cheeseburger sits under the heater.arrow_forwardWhich of the following are specified by the central limit theorem? a. the mean of a specific sample from the distribution of sample means b. the mean of the distribution of sample means c. the shape of the distribution of sample means d. the variability for the distribution of sample meansarrow_forwardQ4-Find the distribution function associated with f(x) = 1, for 0 < x < 1 or 2 < x < 4, and zero elsewhere.arrow_forwardFor a discrete distribution, show that B, 2 B,.arrow_forwardPlease explain:Use your calculator to calculate the following. (P(X > 7), X has an F-distribution with 5 numerator df and 10 denominator df. P(3 < X < 15), X has an F-distribution with 5 numerator df and 10 denominator df.arrow_forwardPlease help with part g, d, and earrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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