A First Course in Probability (10th Edi...10th EditionSheldon Ross Publisher: PEARSONISBN: 9780134753119
A First Course in Probability (10th Edi...
Solutions for A First Course in Probability (10th Edition)
Problem 5.1P:
Let X be a random variable with probability density function f(x)={c(1x2)1x00otherwise a. What is...Problem 5.4P:
The probability density function of X. the lifetime of a certain type of electronic device (measured...Problem 5.7P:
The density function of X is given by f(x)={a+bx20x10otherwise . If E[X]=35, find a and b.Problem 5.8P:
The lifetime in hours of an electronic tube is a random variable having a probability density...Problem 5.9P:
Consider Example 4b &I of Chapter 4 &I, but now suppose that the seasonal demand is a continuous...Problem 5.10P:
Trains headed for destination A arrive at the train station at 15-minute intervals starting at 7...Problem 5.11P:
A point is chosen at random on a line segment of length L. Interpret this statement, and find the...Problem 5.12P:
A bus travels between the two cities A and B. which are 100 miles apart. If the bus has a breakdown,...Problem 5.13P:
You arrive at a bus stop at 10A.M., knowing that the bus will arrive at some time uniformly...Problem 5.14P:
Let X be a uniform (0, 1) random variable. Compute E[Xn] by using Proposition 2.1, and then check...Problem 5.15P:
If X is a normal random variable with parameters =10 and 2=36, compute a. P{X5}; b. P{4X16}; c....Problem 5.16P:
The annual rainfall (in inches) in a certain region is normally distributed with =40 and =4. What is...Problem 5.17P:
The salaries of physicians in a certain speciality are approximately normally distributed. If 25...Problem 5.18P:
Suppose that X is a normal random variable with mean 5. If P{X9}=.2, approximately what is Var(X)?Problem 5.19P:
Let be a normal random variable with mean 12 and variance 4. Find the value of c such that...Problem 5.20P:
If 65 percent of the population of a large community is in favor of a proposed rise in school taxes,...Problem 5.21P:
Suppose that the height, in inches, of a 25-year-old man is a normal random variable with parameters...Problem 5.22P:
Every day Jo practices her tennis serve by continually serving until she has had a total of 50...Problem 5.23P:
One thousand independent rolls of a fair die will be made. Compute an approximation to the...Problem 5.24P:
The lifetimes of interactive computer chips produced by a certain semiconductor manufacturer are...Problem 5.25P:
Each item produced by a certain manufacturer is, independently, of acceptable quality with...Problem 5.26P:
Two types of coins are produced at a factory: a fair coin and a biased one that comes up heads 55...Problem 5.27P:
In 10,000 independent tosses of a coin, the coin landed on heads 5800 times. Is it reasonable to...Problem 5.28P:
Twelve percent of the population is left handed. Approximate the probability that there are at least...Problem 5.29P:
A model for the movement of a stock supposes that if the present price of the stock is s, then after...Problem 5.30P:
An image is partitioned into two regions, one white and the other black. A reading taken from a...Problem 5.31P:
a. A fire station is to be located along a road of length A,A. If fires occur at points uniformly...Problem 5.32P:
The time (in hours) required to repair a machine is an exponentially distributed random variable...Problem 5.34P:
Jones figures that the total number of thousands of miles that a racing auto can be driven before it...Problem 5.36P:
The lung cancer hazard rate (t) of a t-year-old male smoker is such that (t)=.027+.00025(t40)2t40...Problem 5.37P:
Suppose that the life distribution of an item has the hazard rate function (t)=t3,t0. What is the...Problem 5.38P:
If X is uniformly distributed over (1,1), find (a) P{|X|12} (b) the density function of the random...Problem 5.40P:
If X is an exponential random variable with parameter =1, compute the probability density function...Problem 5.43P:
Find the distribution of R=Asin, where A is a fixed constant and is uniformly distributed on (2,2)....Problem 5.44P:
Let Y be a log normal random variable (see Example 7e for its definition) and let c0 be a constant....Problem 5.1TE:
The speed of a molecule in a uniform gas at equilibrium is a random variable whose probability...Problem 5.3TE:
Show that if X has density function f. then E[g(X)]=g(x)f(x)dx Hint: Using Theoretical Exercise 5.2,...Problem 5.5TE:
Use the result that for a nonnegative random variable E[Y]=0P{Yt}dt to show that for a nonnegative...Problem 5.7TE:
The standard deviation of X. denoted SD(X), is given by SD(X)=Var(X). Find SD(aX+b) if X has...Problem 5.8TE:
Let X be a random variable that takes on values between 0 and c. That is,p{0Xc}=1 .Show that...Problem 5.9TE:
Show that Z is a standard normal random variable; then, for x0. a. P{Zx}=P{Zx} b. P{|Z|x}=2P{Zx} c....Problem 5.10TE:
Let f(x) denote the probability density function of a normal random variable with mean , and...Problem 5.11TE:
Let Z be a standard normal random variable Z and let g be a differentiable function with derivative...Problem 5.12TE:
Use the identity of Theoretical Exercises 5.5 .Problem 5.13TE:
The median of a continuous random variable having distribution function F is that value m such that...Problem 5.14TE:
The mode of a continuous random variable having density f is the value of x for which f (x) attains...Problem 5.15TE:
If X is an exponential random variable with parameter , and c0, show that cX is exponential with...Problem 5.17TE:
If X has hazard rate function X(t), compute the hazard rate function of aX where a is a positive...Problem 5.19TE:
If X is an exponential random variable with mean 1, show that E[Xk]=k!kk=1,2,... Hint: Make use of...Problem 5.22TE:
Compute the hazard rate function of a gamma random variable with parameters (,) and show it is...Problem 5.23TE:
Compute the hazard rate function of a Weibull random variable and show it is increasing when 1 and...Problem 5.25TE:
Let Y=(Xv) Show that if X is a Weibull random variable with parameters v,, and , then Y is an...Problem 5.26TE:
Let F be a continuous distribution function. If U is uniformly distributed on (0,1), find the...Problem 5.27TE:
If X is uniformly distributed over (a,b), what random variable, having a linear relation with X. is...Problem 5.28TE:
Consider the beta distribution with parameters (a,b). Show that a. when a1 and b1, the density is...Problem 5.32TE:
Let X and Y be independent random variables that are both equally likely to be either 1,2,...,(10)N...Problem 5.1STPE:
The number of minutes of playing time of a certain high school basketball player in a randomly...Problem 5.5STPE:
The random variable X is said to be a discrete uniform random variable on the integers 1.2..... n if...Problem 5.7STPE:
To be a winner in a certain game, you must be successful in three successive rounds. The game...Problem 5.8STPE:
A randomly chosen IQ test taker obtains a score that is approximately a normal random variable with...Problem 5.9STPE:
Suppose that the travel time from your home to your office is normally distributed with mean 40...Problem 5.10STPE:
The life of a certain type of automobile tire is normally distributed with mean 34,000 miles and...Problem 5.11STPE:
The annual rainfall in Cleveland, Ohio, is approximately a normal random variable with mean 40.2...Problem 5.15STPE:
The number of years that a washing machine functions is a random variable whose hazard rate function...Problem 5.18STPE:
There are two types of batteries in a bin. When in use, type i batteries last (in hours) an...Problem 5.20STPE:
For any real number y define byy+=y,ify00,ify0 Let c be a constant. a. Show that...Problem 5.21STPE:
With (x) being the probability that a normal random variable with mean 0 and variance 1 is less than...Browse All Chapters of This Textbook
Chapter 1 - Combinatorial AnalysisChapter 2 - Axioms Of ProbabilityChapter 3 - Conditional Probability And IndependenceChapter 4 - Random VariablesChapter 5 - Continuous Random VariablesChapter 6 - Jointly Distributed Random VariablesChapter 7 - Properties Of ExpectationChapter 8 - Limit TheoremsChapter 9 - Additional Topics In ProbabilityChapter 10 - Simulation
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EBK A FIRST COURSE IN PROBABILITY
9th Edition
ISBN: 9780321926678
A First Course In Probability
9th Edition
ISBN: 9789332519077
EBK A FIRST COURSE IN PROBABILITY
9th Edition
ISBN: 8220101467447
A First Course in Probability
9th Edition
ISBN: 9780321794772
A First Course In Probability
5th Edition
ISBN: 9780137463145
A First Course in Probability
8th Edition
ISBN: 9780136033134
A First Course In Probability, Global Edition
10th Edition
ISBN: 9781292269207
FIRST COURSE IN PROBABILITY (LOOSELEAF)
10th Edition
ISBN: 9780134753751
EBK FIRST COURSE IN PROBABILITY, A
10th Edition
ISBN: 9780134753676
EBK FIRST COURSE IN PROBABILITY, A
10th Edition
ISBN: 9780134753683
A Second Course in Probability
7th Edition
ISBN: 9780979570407
First Course In Probability, A (7th Edition)
7th Edition
ISBN: 9780131856622
A First Course In Probability (6th Edition)
6th Edition
ISBN: 9780130338518
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