(a) For what value of the constant cis the following function aprobability density function?x > 1f(x) =x < 1(b) Given the value of c that you found in part (a), what is the mean,H, of this probability density function?

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Answered: (a) For what value of the constant c is…

A First Course in Probability (10th Edition)

10th Edition

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Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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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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Question 2. A continuous random variable, X has the following probability density function: S(x) = cx² 0sxs10 = 0 otherwise a) Find the value of c. b) Find the mean, median, mode, standard deviation and coefficient of variation. c) Find the probability that X is greater than 3.0 given that X is between 2.0 and 5.0.
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The probability density function of the time a customer arrives at a terminal (in minutes after 8:00 A.M.) is f(x) = 0.25 e-x/4 for x > 0. Determine the probability that(a) The customer arrives by 10:00 A.M. (Round your answer to one decimal place (e.g. 98.7))(b) The customer arrives between 8:19 A.M. and 8:31 A.M. (Round your answer to four decimal places (e.g. 98.7654))(c) Determine the time (in hours A.M. as decimal) at which the probability of an earlier arrival is 0.51. (Round your answer to two decimal places (e.g. 98.76))(d) Determine the cumulative distribution function and use the cumulative distribution function to determine the probability that the customer arrives between 8:19 A.M. and 8:31 A.M. (Round your answer to four decimal places (e.g. 98.7654))(e) Determine the mean and (f) standard deviation of the number of minutes until the customer arrives. (Round your answers to one decimal place (e.g. 98.7))
Section: Probabilty Density Functions

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(a) For what value of the constant c is the following function a probability density function? x > 1 f(x) = x < 1 (b) Given the value of c that you found in part (a), what is the mear µ, of this probability density function?