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Roughly, speaking, we can use probability density functions to model the likelihood of an vent occurring. Formally, a probability density function on (-o0, 0) is a function f such hat S(2) 2 0 and s(=) = 1. a) Determine which of the following functions are probability density functions on the (-x, 00). (i) f(x) = otherwise -2 0< z < 2v2 (ii) f(x) = { (z - v2)³ otherwise de 00

Roughly, speaking, we can use probability density functions to model the likelihood of an vent occurring. Formally, a probability density function on (-o0, 0) is a function f such hat S(2) 2 0 and s(=) = 1. a) Determine which of the following functions are probability density functions on the (-x, 00). (i) f(x) = otherwise -2 0< z < 2v2 (ii) f(x) = { (z - v2)³ otherwise de 00

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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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(2) 20 and Lsla) = 1. (a) Determine which of the following functions are probability density functions on the (-00, 00). (1-1 0<I<e (i) f(x) = otherwise -2 0<1< 2/2 (ii) f(x) = { (z- /2)³ otherwise (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. zf(z) dz yields the expected value for a density f(x) with domain on the real mumbers.) 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(2) 20 and Lsla) = 1. (a) Determine which of the following functions are probability density functions on the (-00, 00). (1-1 0<I<e (i) f(x) = otherwise -2 0<1< 2/2 (ii) f(x) = { (z- /2)³ otherwise (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. zf(z) dz yields the expected value for a density f(x) with domain on the real mumbers.) Find the expected value for one of the valid probability densities above.
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