Roughly, speaking, we can use probability density functions to model the likelihood of an event occurring. Formally, a probability density function on (-x, 0) is a function f such hat S(z) 20 and | (2) = 1. a) Determine which of the following functions are probability density functions on the (-0, 00). r- 00 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. f(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.
Roughly, speaking, we can use probability density functions to model the likelihood of an event occurring. Formally, a probability density function on (-x, 0) is a function f such hat S(z) 20 and | (2) = 1. a) Determine which of the following functions are probability density functions on the (-0, 00). r- 00 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. f(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.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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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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