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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 f such that f (x) > 0 and | f(x) = 1. (a) Determine which of the following functions are probability density functions on the (-00, 00). 0 < x < e (i) f(x) = otherwise -2 0 < x < 2/2 V2)3 (ii) ƒ(x) = { (x – v otherwise (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. S 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 (-0, ∞) 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, 00). 0 < x < e (i) f(x) = otherwise -2 0 < x < 2/2 V2)3 (ii) ƒ(x) = { (x – v otherwise (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. S 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.

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
ChapterP: Prerequisites
SectionP.6: Analyzing Graphs Of Functions
Problem 6ECP: Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.
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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 f such that f (x) > 0 and | f(x) = 1. (a) Determine which of the following functions are probability density functions on the (-00, 00). 0 < x < e (i) f(x) = otherwise -2 0 < x < 2/2 V2)3 (ii) ƒ(x) = { (x – v otherwise (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. S 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, ∞) 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, 00). 0 < x < e (i) f(x) = otherwise -2 0 < x < 2/2 V2)3 (ii) ƒ(x) = { (x – v otherwise (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. S 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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