Problem 8.1P: Suppose that X is a random variable with mean and variance both equal to 20. What can be said about... Problem 8.2P: From past experience, a professor knows that the test score of a student taking her final... Problem 8.3P: Use the central limit theorem to solve part (c) of Problem 8.2. Problem 8.4P: Let X1,...,X20 be independent Poisson random variables with mean 1. a. Use the Markov inequality to... Problem 8.5P: Fifty numbers are rounded off to the nearest integer and then summed. If the individual round-off... Problem 8.6P: A die is continually rolled until the total sum of all rolls exceeds 300. Approximate the... Problem 8.7P: A person has 100 light bulbs whose lifetimes are independent exponentials with mean 5 hours. If the... Problem 8.8P: In Problem 8.7, suppose that it takes a random time, uniformly distributed over (0, .5), to replace... Problem 8.9P: If X is a gamma random variable with parameters (n,1), approximately how large must n be so that... Problem 8.10P: Civil engineers believe that W, the amount of weight (in units of 1000 pounds) that a certain span... Problem 8.11P: Many people believe that the daily change of price of a companys stock on the stock market is a... Problem 8.12P: We have 100 components that we will put in use in a sequential fashion. That is, component 1 is... Problem 8.13P: Student scores on exams given by a certain instructor have mean 74 and standard deviation 14. This... Problem 8.14P: A certain component is critical to the operation of an electrical system and must be replaced... Problem 8.15P: An insurance company has 10.000 automobile policyholders. The expected yearly claim per policyholder... Problem 8.16P: A.J. has 20 jobs that she must do in sequence, with the times required to do each of these jobs... Problem 8.17P: Redo Example 5b under the assumption that the number of man—woman pairs is (approximately)... Problem 8.18P: Repeat part (a) of Problem 8.2 when it is known that the variance of a students test score is equal... Problem 8.19P: A lake contains 4 distinct types of fish. Suppose that each fish caught is equally likely to be any... Problem 8.20P: If X is a nonne9ative random variable with mean 25, what can be said about a. E[X3]? b. E[X]? c.... Problem 8.21P: Let X be a nonnegative random variable. Prove that E[X](E[X2])12(E[X3])13... Problem 8.22P Problem 8.23P: Let X be a Poisson random variable with mean 20. a. Use the Markov inequality to obtain an upper... Problem 8.24P Problem 8.25P Problem 8.26P: If f(x) is an Increasing and g(x) is a decreasing function, show that E[f(X)g(X)]E[f(X)E][g(X)]. Problem 8.27P: If L(p) is the Lorenz curve associated with the random variable X, show thatL(p)=E[X][Xp]pE[X] Problem 8.28P: Suppose that L(p) is the Lorenz curve associated with the random variable X and thatc0. a. Find the... Problem 8.1TE: If X has variance 2, then , the positive square root of the variance, is called the standard... Problem 8.2TE: If X has mean and standard deviation , the ratio r|| is called the measurement signal-to-noise... Problem 8.3TE: Compute the measurement signal-to-noise ratio-that is ||, where =E[X] and 2=var(X) -of the following... Problem 8.4TE: Let Zn,n1, be a sequence of random variables and ca constant such that for each0,P{|Znc|}0 as n.... Problem 8.5TE Problem 8.6TE Problem 8.7TE Problem 8.8TE: Explain why a gamma random variable with parameters (t,) has an approximately normal distribution... Problem 8.9TE Problem 8.10TE: If X is a Poisson random variable with mean , show that for i, P{Xi}e(e)iii Problem 8.11TE Problem 8.12TE Problem 8.13TE Problem 8.14TE Problem 8.15TE: If f and g are density functions that are positive over the same region, then the kullback-leiber... Problem 8.16TE Problem 8.1STPE: The number of automobiles sold weekly at a certain dealership is a random variable with expected... Problem 8.2STPE Problem 8.3STPE: If E[X]=75E[Y]=75Var(X)=10var(Y)=12cov(X,Y)=3 give an upper bound to a. P{|XY|15}; b. P{XY+15}; c.... Problem 8.4STPE Problem 8.5STPE Problem 8.6STPE Problem 8.7STPE Problem 8.8STPE Problem 8.9STPE Problem 8.10STPE: A tobacco company claims that the amount of nicotine in one of its cigarettes is a random variable... Problem 8.11STPE Problem 8.12STPE Problem 8.13STPE: The strong law of large numbers states that with probability 1, the successive arithmetic averages... Problem 8.14STPE: Each new book donated to a library must be processed. Suppose that the time it takes to process a... Problem 8.15STPE: Prove Chebyshevs sum inequality, which says that if a1a2...an and b1b2...bn, then... format_list_bulleted
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