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Roughly, speaking, we can use probability density functions to model the likelihood of an event occurring. Formally, a probability density function on (-0, 00) is a function f such that f (x) > 0 and roo | f(x) = 1. (a) Determine which of the following functions are probability density functions on the (-∞, 00). 0 < x < e (i) f(x) = otherwise -2 0 < x < 2/2 (ii) ƒ(x) = (x – v2)3 otherwise Aeda 0< x < ∞ (iii) f(x) = otherwise where A> 0

Roughly, speaking, we can use probability density functions to model the likelihood of an event occurring. Formally, a probability density function on (-0, 00) is a function f such that f (x) > 0 and roo | f(x) = 1. (a) Determine which of the following functions are probability density functions on the (-∞, 00). 0 < x < e (i) f(x) = otherwise -2 0 < x < 2/2 (ii) ƒ(x) = (x – v2)3 otherwise Aeda 0< x < ∞ (iii) f(x) = otherwise where A> 0

Calculus: Early Transcendentals
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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Roughly, speaking, we can use probability density functions to model the likelihood of an event occurring. Formally, a probability density function on (-∞,00) is a function f such that f(x) > 0 and | f(x) = 1. (a) Determine which of the following functions are probability density functions on the (-00, 0). -1 0 < x < e (i) f(x) = otherwise -2 0 < x < 2/2 (ii) ƒ(x) = (x – /2)3 otherwise ela 0 < x < ∞ (iii) f(x) = - otherwise where A> 0 (b) We can also use probability density functions to find the expected value of the outcomes of the event - if we repeated a probability experiment many times, the expected value will equal the average of the outcomes of the experiment. (e.g. , xf (x) dx yields the expected value for a density f(x) with domain on the real numbers.) Find the expected value for one of the valid probability densities above.
Transcribed Image Text:Roughly, speaking, we can use probability density functions to model the likelihood of an event occurring. Formally, a probability density function on (-∞,00) is a function f such that f(x) > 0 and | f(x) = 1. (a) Determine which of the following functions are probability density functions on the (-00, 0). -1 0 < x < e (i) f(x) = otherwise -2 0 < x < 2/2 (ii) ƒ(x) = (x – /2)3 otherwise ela 0 < x < ∞ (iii) f(x) = - otherwise where A> 0 (b) We can also use probability density functions to find the expected value of the outcomes of the event - if we repeated a probability experiment many times, the expected value will equal the average of the outcomes of the experiment. (e.g. , xf (x) dx yields the expected value for a density f(x) with domain on the real numbers.) Find the expected value for one of the valid probability densities above.
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