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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) is a function ƒ such that f(x) > 0 and | f(x) = 1. (a) Determine which of the following functions are probability density functions on the (-0, 00). x-1 0 0

Roughly, speaking, we can use probability density functions to model the likelihood of an event occurring. Formally, a probability density function on (-∞,0) is a function ƒ such that f(x) > 0 and | f(x) = 1. (a) Determine which of the following functions are probability density functions on the (-0, 00). x-1 0 0

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 29CR
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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, 0) is a function ƒ such that f(x) > 0 and | f(x) = 1. (a) Determine which of the following functions are probability density functions on the (-0, 00). 0 < x < e (i) f(x) = otherwise -2 0 < x < 2/2 (ii) ƒ(x) = (x – /2)3 otherwise dedx 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. L 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 (-0, 0) is a function ƒ such that f(x) > 0 and | f(x) = 1. (a) Determine which of the following functions are probability density functions on the (-0, 00). 0 < x < e (i) f(x) = otherwise -2 0 < x < 2/2 (ii) ƒ(x) = (x – /2)3 otherwise dedx 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. L 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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