completing the proof. Example 2.1.1 Let 2 = R, ar - F(x) by O You are sharing your entire screen. Stop Sharing on R. Define please prove pant citi) = P((-0, x]), x € R. (2.3) X, { xq →F(4)< Fras) Then R() F is right continuous, K Becnse (ii) F is monotone non-decreasing, (iii) F has limits at ±00 F (∞0) := lim F(x) = 1 xt00 F(-0) := lim F(x)= 0. 00-tx Definition 2.1.1 A function F : R → [0, 1] satisfying (i), (ii), (iii) is called a (probability) distribution function. We abbreviate distribution function by df. 28
completing the proof. Example 2.1.1 Let 2 = R, ar - F(x) by O You are sharing your entire screen. Stop Sharing on R. Define please prove pant citi) = P((-0, x]), x € R. (2.3) X, { xq →F(4)< Fras) Then R() F is right continuous, K Becnse (ii) F is monotone non-decreasing, (iii) F has limits at ±00 F (∞0) := lim F(x) = 1 xt00 F(-0) := lim F(x)= 0. 00-tx Definition 2.1.1 A function F : R → [0, 1] satisfying (i), (ii), (iii) is called a (probability) distribution function. We abbreviate distribution function by df. 28
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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63% O
Thu 17:12
A Resnick_book.pdf (page 47 of 464)
IPEVO
Q Search
DOther Bool
completing the proof.
Example 2.1.1 Let 2 = R, ar
F(x) by
on R. Define
%3D
O You are sharing your entire screen.
Stop Sharing
pp presenti
please
prove pant (F) = P(-0, x), x€ R.
(2.3)
X, < x2 →F(4) Frag)
→ F(4)<
Then
di
(i) F is right continuous,
2 Beaoe
(ii) F is monotone non-decreasing,
eh
(iii) F has limits at ±00
F(∞) := lim F(x) = 1
F(-0) := lim F(x) = 0.
x1-00
Fean) { Flaz)
Definition 2.1.1 A function F : R → [0, 1] satisfying (i), (ii), (iii) is called a
(probability) distribution function. We abbreviate distribution function by df.
28](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbb3963ff-d7bd-40ff-82ca-f7552015f1bb%2Fcff60d05-b341-4076-8204-6ef72db6380c%2Fukork75_processed.png&w=3840&q=75)
Transcribed Image Text:Preview
File
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63% O
Thu 17:12
A Resnick_book.pdf (page 47 of 464)
IPEVO
Q Search
DOther Bool
completing the proof.
Example 2.1.1 Let 2 = R, ar
F(x) by
on R. Define
%3D
O You are sharing your entire screen.
Stop Sharing
pp presenti
please
prove pant (F) = P(-0, x), x€ R.
(2.3)
X, < x2 →F(4) Frag)
→ F(4)<
Then
di
(i) F is right continuous,
2 Beaoe
(ii) F is monotone non-decreasing,
eh
(iii) F has limits at ±00
F(∞) := lim F(x) = 1
F(-0) := lim F(x) = 0.
x1-00
Fean) { Flaz)
Definition 2.1.1 A function F : R → [0, 1] satisfying (i), (ii), (iii) is called a
(probability) distribution function. We abbreviate distribution function by df.
28
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