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6. Roughly, speaking, we can use probability density functions to model the likelihood of an event occurring. Formally, a probability density function on (-0o, 00) is a function f such that f(x) 2 0 and f(x) = 1. %3D (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 (ii) f(x) = (x - v2)3 0. otherwise leta 0 0

6. Roughly, speaking, we can use probability density functions to model the likelihood of an event occurring. Formally, a probability density function on (-0o, 00) is a function f such that f(x) 2 0 and f(x) = 1. %3D (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 (ii) f(x) = (x - v2)3 0. otherwise leta 0 0

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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6. Roughly, speaking, we can use probability density functions to model the likelihood of an event occurring. Formally, a probability density function on (-oo, 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 (-0, 00). x-1 0<x < e (i) ƒ(x) = 10 otherwise -2 0 < x < 2v2 (ii) f(x) = { (x – v2)3 0. otherwise Aeda 0<x < ∞ dedzo (iii) f(x) = 0. 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) dr 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:6. Roughly, speaking, we can use probability density functions to model the likelihood of an event occurring. Formally, a probability density function on (-oo, 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 (-0, 00). x-1 0<x < e (i) ƒ(x) = 10 otherwise -2 0 < x < 2v2 (ii) f(x) = { (x – v2)3 0. otherwise Aeda 0<x < ∞ dedzo (iii) f(x) = 0. 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) dr 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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