"Question 1. Continuous Probability Distributions [.1Let X denote the length of a randomly selected phone call (in minutes). The probability densityfunction of X is f(x),xe R.(a) Show that f(x) is a probability density function.(b) What is the probability that the length of phone call is more than 3 minutes?(c) Find the probability P(2 < X<5).(d) Find the expected value (mean) of X.(e) Find the standard deviation of X.(f) Derive the cumulative distribution function of X, F(x).Probability density function f(x) andrange Rx6f(x) = rsx(x −3), Ry:0$xs5

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Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Let X denote the length of a randomly selected phone call (in minutes). The probability density function of X is f(x), xe R₁. (a) Show that f(x) is a probability density function. (b) What is the probability that the length of phone call is more than 3 minutes? (c) Find the probability P(2< X<5).