6. Roughly, speaking, we can use probability density functions to model the likelihood of an event occurring. Formally, a probability density function on (-o, 0) is a function f such that f(r) 20 and f(2) = = 1. (a) Determine which of the following functions are probability density functions on the (-00, 00). (1 00 (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. af(x) dr yields the expected value for a density f(r) with domain on the real numbers.) Find the expected value for one of the valid probability densities above.
6. Roughly, speaking, we can use probability density functions to model the likelihood of an event occurring. Formally, a probability density function on (-o, 0) is a function f such that f(r) 20 and f(2) = = 1. (a) Determine which of the following functions are probability density functions on the (-00, 00). (1 00 (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. af(x) dr yields the expected value for a density f(r) with domain on the real numbers.) Find the expected value for one of the valid probability densities above.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 (-x, o0) is a function f such
that
f(r) 20
and
(2) =
= 1.
(a) Determine which of the following functions are probability density functions on the
(-x0, 00).
fr-1 0<r<e
(i) f(x) =
otherwise
-2
0 < r < 2/2
(ii) f(x) =
(r – V2)3
otherwise
Aedz 0<r<0
(iii) f(2) =
otherwise
where A>0
(b) We can also use probability density functions to find the erpected 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. rf(x) dr yields the
expected value for a density f(r) with domain on the real numbers.) Find the expected
value for one of the valid probability densities above.
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