For the probability density function f defined on the random variable x, find (a) the mean of x, (b) the standard deviation of x, and (c) the probability that the random variable x is within one standard deviation ofthe mean.1f(x) =x, [5,9]28a) Find the mean.%3D(Round to three decimal places as needed.)b) Find the standard deviation.(Round to three decimal places as needed.)c) Find the probability that the random variable x is within one standard deviation of the mean.The probability is.(Round to three decimal places as needed.)

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Answered: a) Find the mean. (Round to three…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Determine if the following statements are true or false. a. Jane took a sample of n = 100 observations from a population with mean and standard deviation. Mike also took a sample of n = 200 observations from the same population. Then, Mike’s sample mean will be closer to the true population mean than Jane’s sample. b. Jane took a sample of n = 100 observations from a population with mean and standard deviation. Mike also took a sample of n = 200 observations from a population with mean and standard deviation 2. Then, the sample mean from Mike’s sample is more likely to be close to the true mean than the sample mean from Jane’s sample. That is, the probability that X is between 90% and 110% of mean is higher for Mike’s sample than for Jane’s sample.

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a) Find the mean. (Round to three decimal places as needed.) b) Find the standard deviation. (Round to three decimal places as needed.) c) Find the probability that the random variable x is within one standard deviation of the mean. The probability is: (Round to three decimal places as needed.)