A First Course In Probability, Global Edition
10th Edition
ISBN: 9781292269207
Author: Ross, Sheldon
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Question
Chapter 5, Problem 5.30TE
To determine
To find: The expected lifetime of an electronic tube.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Let X be a random variable with the probability density function.
f(r) =
2c
for x = 1,2,3, 4, ..., 0
for some constant c. What is the value of c What is the probability that X is even?
Let y be the random variable with the time to hear an owl from your room's open window (in
hours). Assume that the probability that you still need to wait to hear the owl after y hours is
one of the following: the probability is given by 0. 47e-4y + 0. 52e-5y
Find the probability that you need to wait between 2 and 4 hours to hear the owl, compute
and display the probability density function graph as well as a histogram by the minute.
Compute and display in the graphics the mean, variance, and quartiles of the waiting times.
Please pay attention to the various units of time!
Let X and Y be two continuous random variables with joint probability density function f(x,y) = 2xy for 0 < x < y < 1. Find the covariance between X and Y.
Chapter 5 Solutions
A First Course In Probability, Global Edition
Ch. 5 - Let X be a random variable with probability...Ch. 5 - Prob. 5.2PCh. 5 - Prob. 5.3PCh. 5 - The probability density function of X. the...Ch. 5 - Prob. 5.5PCh. 5 - Compute E[X] if X has a density function given by...Ch. 5 - The density function of X is given by...Ch. 5 - The lifetime in hours of an electronic tube is a...Ch. 5 - Consider Example 4b &I of Chapter 4 &I, but now...Ch. 5 - Trains headed for destination A arrive at the...
Ch. 5 - A point is chosen at random on a line segment of...Ch. 5 - A bus travels between the two cities A and B....Ch. 5 - You arrive at a bus stop at 10A.M., knowing that...Ch. 5 - Let X be a uniform (0, 1) random variable. Compute...Ch. 5 - If X is a normal random variable with parameters...Ch. 5 - The annual rainfall (in inches) in a certain...Ch. 5 - The salaries of physicians in a certain speciality...Ch. 5 - Suppose that X is a normal random variable with...Ch. 5 - Let be a normal random variable with mean 12 and...Ch. 5 - If 65 percent of the population of a large...Ch. 5 - Suppose that the height, in inches, of a...Ch. 5 - Every day Jo practices her tennis serve by...Ch. 5 - One thousand independent rolls of a fair die will...Ch. 5 - The lifetimes of interactive computer chips...Ch. 5 - Each item produced by a certain manufacturer is,...Ch. 5 - Two types of coins are produced at a factory: a...Ch. 5 - In 10,000 independent tosses of a coin, the coin...Ch. 5 - Twelve percent of the population is left handed....Ch. 5 - A model for the movement of a stock supposes that...Ch. 5 - An image is partitioned into two regions, one...Ch. 5 - a. A fire station is to be located along a road of...Ch. 5 - The time (in hours) required to repair a machine...Ch. 5 - If U is uniformly distributed on (0,1), find the...Ch. 5 - Jones figures that the total number of thousands...Ch. 5 - Prob. 5.35PCh. 5 - The lung cancer hazard rate (t) of a t-year-old...Ch. 5 - Suppose that the life distribution of an item has...Ch. 5 - If X is uniformly distributed over (1,1), find (a)...Ch. 5 - Prob. 5.39PCh. 5 - If X is an exponential random variable with...Ch. 5 - If X is uniformly distributed over(a,b), find a...Ch. 5 - Prob. 5.42PCh. 5 - Find the distribution of R=Asin, where A is a...Ch. 5 - Let Y be a log normal random variable (see Example...Ch. 5 - The speed of a molecule in a uniform gas at...Ch. 5 - Show that E[Y]=0P{Yy}dy0P{Yy}dy Hint: Show that...Ch. 5 - Show that if X has density function f. then...Ch. 5 - Prob. 5.4TECh. 5 - Use the result that for a nonnegative random...Ch. 5 - Prob. 5.6TECh. 5 - The standard deviation of X. denoted SD(X), is...Ch. 5 - Let X be a random variable that takes on values...Ch. 5 - Show that Z is a standard normal random variable;...Ch. 5 - Let f(x) denote the probability density function...Ch. 5 - Let Z be a standard normal random variable Z and...Ch. 5 - Use the identity of Theoretical Exercises 5.5 .Ch. 5 - The median of a continuous random variable having...Ch. 5 - The mode of a continuous random variable having...Ch. 5 - If X is an exponential random variable with...Ch. 5 - Compute the hazard rate function of X when X is...Ch. 5 - If X has hazard rate function X(t), compute the...Ch. 5 - Prob. 5.18TECh. 5 - If X is an exponential random variable with mean...Ch. 5 - Prob. 5.20TECh. 5 - Prob. 5.21TECh. 5 - Compute the hazard rate function of a gamma random...Ch. 5 - Compute the hazard rate function of a Weibull...Ch. 5 - Prob. 5.24TECh. 5 - Let Y=(Xv) Show that if X is a Weibull random...Ch. 5 - Let F be a continuous distribution function. If U...Ch. 5 - If X is uniformly distributed over (a,b), what...Ch. 5 - Consider the beta distribution with parameters...Ch. 5 - Prob. 5.29TECh. 5 - Prob. 5.30TECh. 5 - Prob. 5.31TECh. 5 - Let X and Y be independent random variables that...Ch. 5 - Prob. 5.33TECh. 5 - The number of minutes of playing time of a certain...Ch. 5 - For some constant c. the random variable X has the...Ch. 5 - Prob. 5.3STPECh. 5 - Prob. 5.4STPECh. 5 - The random variable X is said to be a discrete...Ch. 5 - Prob. 5.6STPECh. 5 - To be a winner in a certain game, you must be...Ch. 5 - A randomly chosen IQ test taker obtains a score...Ch. 5 - Suppose that the travel time from your home to...Ch. 5 - The life of a certain type of automobile tire is...Ch. 5 - The annual rainfall in Cleveland, Ohio, is...Ch. 5 - Prob. 5.12STPECh. 5 - Prob. 5.13STPECh. 5 - Prob. 5.14STPECh. 5 - The number of years that a washing machine...Ch. 5 - Prob. 5.16STPECh. 5 - Prob. 5.17STPECh. 5 - There are two types of batteries in a bin. When in...Ch. 5 - Prob. 5.19STPECh. 5 - For any real number y define byy+=y,ify00,ify0 Let...Ch. 5 - With (x) being the probability that a normal...Ch. 5 - Prob. 5.22STPECh. 5 - Letf(x)={13ex1313e(x1)ifx0if0x1ifx1 a. Show that f...Ch. 5 - Prob. 5.24STPE
Knowledge Booster
Similar questions
- Let X be a point randomly chosen on a stick of length 1 with a uniform distribution. Let Y be a point chosen between 0 and X on this stick with a uniform distribution. Y X 1 Find the conditional probability density function (and the range) of X given Y = y. Please provide the solution step by step.arrow_forwardThe life lengths of two transistors in an electronic circuit is a random vector (X; Y) where X is the life length of transistor 1 and Y is the life length of transistor 2. The joint probability density function of (X; Y) is given by x 2 0, y 2 0 fx.,fx.v) = 20 else Then the probability that the first transistor burned during half hour given that the second one lasts at least half hour equals Select one: a. 0.606 b. 0.3935 C. 0.6318 d. 0.3669 e. 0.7772arrow_forwardThe probability density of the random variable Z isgiven by f(z) = kze−z2for z > 00 for z F 0Find k and draw the graph of this probability density.arrow_forward
- The probability density function of the continuous random variable X defined in the set of non-negative real numbers is given as f(x) = 2.exp(-2x). What is the expected value of X?arrow_forwardDetermine the mean and variance of the random variable with the probability density function f (x) = 1.6(1 − 0.8 x), 0 < x ≤ 1.25.arrow_forwardThe random variable X has a uniform density function over the interval [-1, 1]. a. Sketch the probability density function of X. Find the mean and variance of X .arrow_forward
- Let X be a point randomly chosen on a stick of length 1 with a uniform distribution. Let Y be a point chosen between 0 and X on this stick with a uniform distribution. Y X 1 Find the joint probability density function (and the joint range) of X and Y. Please provide the solution step by step.arrow_forwarda probability density function A continuous random variable X, with mean unity, has probability density function fx(x) given by 0≤x≤ b, fx(x) = (a(b-x)², 10, otherwise. Find the values of a and b.arrow_forwardLet X be a random variable that follows U (0, 2). Define another random variable Y such that Y = – In X. What is the cumulative distribution function of Y? What is the probability density function of Y?arrow_forward
- let X denotes the percentage of time out of a 40-hour workweek that a call center agent is directly serving a client by answering phone calls. Suppose that X has a probability density function defined by f(x) =3x² for 0 ≤ x ≤ 1. Find the mean and variance of X. Interpret the results.arrow_forwardA continuous probability distribution has probability density function f (y) = a (b– y), 0< y < b, and 0 elsewhere. If the mean of the distribution is .2, find the values of a and b a = 1/9 and b= 2) a = 1/72 and b = 12 O a = 1/18 and b= 6 0 a = 2/9 and b = 30 a = 2/81 and b = 90arrow_forwardLet X and Y be two random variables that are independent and have the same probability density function. If U = max (X, Y) V = min (X, Y), find the distribution function of the U random variable using the distribution function technique.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill