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