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Like French: “A vaincre sans péril, on triomphe sans gloire.” – Corneille
Meaning: “To win without risk is a triumph without glory.”
Like C++:
#include <iostream>
using namespace std;
void main() {
cout << "Hello World!" << endl;
cout << "Welcome to C++ Programming" << endl; } Words – Probability models, random variables, expectation ...
Grammar – Axioms, theorems, principles
You have learned it well when you know how to use it M. Chen ([email protected]) ENGG2430 lecture 1 5 / 16 Set Why do we care: Probability use sets and set operations extensively
A set is a collection of objects, which are the elements of the set.
If S is a set and x is an element of S , we write x ∈ S Deﬁning set
S = {x1 , x2 , . . . , xn }
S = {x  x satisﬁes condition P } Example: the set of possible outcomes of a coin toss is {Head, Tail}
Subset: a set S is a subset of another set T , written as S ⊆ T , if
every element of S is also an element of T , e.g.,
S = {all IE students} ⊆ T = {all CU students}
Two sets S and T are equal, written as S = T , if S ⊆ T and T ⊆ S
(a useful proof logic)
M. Chen ([email protected]) ENGG2430 lecture 1 6 / 16 Set Operations The universal set Ω and the empty set 0
/
Complement of a set S
S c = {x ∈ Ωx ∈ S }
/ Union of two sets S and T
S ∪ T = {x x ∈ S or x ∈ T } Intersection of two sets S and T
S ∩ T = {x x ∈ S and x ∈ T } M. Chen ([email protected]) ENGG2430 lecture 1 7 / 16 Set Operations – Examples Deﬁne the universal set Ω = {x  x ∈ (−∞, ∞)}
Deﬁne sets S = {x x > 1}, T = {x x < −2}
Questions:
/
S c = {x ∈ Ωx ∈ S } =?
S ∪ T = {x x ∈ S or x ∈ T } =?
S ∩ T = {x x ∈ S and x ∈ T } =?
S ...
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This document was uploaded on 03/31/2014.
 Spring '14

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