A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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Chapter 8, Problem 8.5STPE
To determine
To find the value of
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Chapter 8 Solutions
A First Course in Probability (10th Edition)
Ch. 8 - Suppose that X is a random variable with mean and...Ch. 8 - From past experience, a professor knows that the...Ch. 8 - Use the central limit theorem to solve part (c) of...Ch. 8 - Let X1,...,X20 be independent Poisson random...Ch. 8 - Fifty numbers are rounded off to the nearest...Ch. 8 - A die is continually rolled until the total sum of...Ch. 8 - A person has 100 light bulbs whose lifetimes are...Ch. 8 - In Problem 8.7, suppose that it takes a random...Ch. 8 - If X is a gamma random variable with parameters...Ch. 8 - Civil engineers believe that W, the amount of...
Ch. 8 - Many people believe that the daily change of price...Ch. 8 - We have 100 components that we will put in use in...Ch. 8 - Student scores on exams given by a certain...Ch. 8 - A certain component is critical to the operation...Ch. 8 - An insurance company has 10.000 automobile...Ch. 8 - A.J. has 20 jobs that she must do in sequence,...Ch. 8 - Redo Example 5b under the assumption that the...Ch. 8 - Repeat part (a) of Problem 8.2 when it is known...Ch. 8 - A lake contains 4 distinct types of fish. Suppose...Ch. 8 - If X is a nonne9ative random variable with mean...Ch. 8 - Let X be a nonnegative random variable. Prove that...Ch. 8 - Prob. 8.22PCh. 8 - Let X be a Poisson random variable with mean 20....Ch. 8 - Prob. 8.24PCh. 8 - Prob. 8.25PCh. 8 - If f(x) is an Increasing and g(x) is a decreasing...Ch. 8 - If L(p) is the Lorenz curve associated with the...Ch. 8 - Suppose that L(p) is the Lorenz curve associated...Ch. 8 - If X has variance 2, then , the positive square...Ch. 8 - If X has mean and standard deviation , the ratio...Ch. 8 - Compute the measurement signal-to-noise ratio-that...Ch. 8 - Let Zn,n1, be a sequence of random variables and...Ch. 8 - Prob. 8.5TECh. 8 - Prob. 8.6TECh. 8 - Prob. 8.7TECh. 8 - Explain why a gamma random variable with...Ch. 8 - Prob. 8.9TECh. 8 - If X is a Poisson random variable with mean , show...Ch. 8 - Prob. 8.11TECh. 8 - Prob. 8.12TECh. 8 - Prob. 8.13TECh. 8 - Prob. 8.14TECh. 8 - If f and g are density functions that are positive...Ch. 8 - Prob. 8.16TECh. 8 - The number of automobiles sold weekly at a certain...Ch. 8 - Prob. 8.2STPECh. 8 - If E[X]=75E[Y]=75Var(X)=10var(Y)=12cov(X,Y)=3 give...Ch. 8 - Prob. 8.4STPECh. 8 - Prob. 8.5STPECh. 8 - Prob. 8.6STPECh. 8 - Prob. 8.7STPECh. 8 - Prob. 8.8STPECh. 8 - Prob. 8.9STPECh. 8 - A tobacco company claims that the amount of...Ch. 8 - Prob. 8.11STPECh. 8 - Prob. 8.12STPECh. 8 - The strong law of large numbers states that with...Ch. 8 - Each new book donated to a library must be...Ch. 8 - Prove Chebyshevs sum inequality, which says that...
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- Recall that the general form of a logistic equation for a population is given by P(t)=c1+aebt , such that the initial population at time t=0 is P(0)=P0. Show algebraically that cP(t)P(t)=cP0P0ebt .arrow_forwardFor a certain psychiatric clinic suppose that the random variable X represents the total time (in minutes) that a typical patient spends in this clinic during a typical visit (where this total time is the sum of the waiting time and the treatment time), and that the random variable Y represents the waiting time (in minutes) that a typical patient spends in the waiting room before starting treatment with a psychiatrist. Further, suppose that X and Y can be assumed to follow the bivariate density function fXY(x,y)=λ2e−λx, 0<y<x, where λ > 0 is a known parameter value. (a) Find the marginal density fX(x) for the total amount of time spent at the clinic. (b) Find the conditional density for waiting time, given the total time. (c) Find P (Y > 20 | X = x), the probability a patient waits more than 20 minutes if their total clinic visit is x minutes. (Hint: you will need to consider two cases, if x < 20 and if x ≥ 20.)arrow_forwardfind the value of the constant c so that the given function is a probability density function for a random variable over the specified interval. . ƒ(x) = 1/ 6 x over [3, c].arrow_forward
- On a production line, parts are produced with a certain average size, but the exact size of each part varies due to the imprecision of the production process. Suppose that the difference between the size of the pieces produced (in millimeters) and the average size, which we will call production error, can be modeled as a continuous random variable X with a probability density function given by f(x) = 2, 5e^(-5|x|), for x E R (is in the image). Parts where the production error is less than -0.46 mm or greater than 0.46 mm should be discarded. Calculate (approximating to 4 decimal places): a) What is the proportion of parts that the company discards in its production process? b) What is the proportion of parts produced where the production error is positive? c) Knowing that for a given part the production error is positive, what is the probability of this part being discarded?arrow_forwardThe length of time for students to complete a 1-hour timed standardized mathematics test has a probability density function f(t) = 1.5t2 + t, 0 ≤ t ≤ 1arrow_forward
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