ECEN 303 - Random Signals Exam 1 (Chapter 1-4) Review (TAMU) fully solved

ECEN 303 - Random Signals Exam 1
(Chapter 1-4) Review (TAMU) fully
solved

Set - correct answer ✔✔ collection of objects



Elements - correct answer ✔✔ Objects of a set



x∈S - correct answer ✔✔ - "x belongs to set S"

- "x is an element of S"



x∉S - correct answer ✔✔ - "x does not belong to set S"

- "x is not an element of S"



x=y - correct answer ✔✔ denote the same object



S⊂T - correct answer ✔✔ S is a subset of T



What is a proper subset? - correct answer ✔✔ - When S is different from T

- S cannot equal T if it is this

- S⊆T



If S⊂T, what are the possible ways that S is related to T - correct answer ✔✔ - S could be equal

- S could be smaller (subset)

- Must be contained in T

, S=T is true if and only if: - correct answer ✔✔ S⊂T and T⊂S



Symbol for "the set of" - correct answer ✔✔ {___}



Symbol for "such that" - correct answer ✔✔ |



Symbol for "all real whole numbers or integers" - correct answer ✔✔ ℤ



Write:

S equals the set of x as an element of whole numbers (integers) such that x is an even number -
correct answer ✔✔ S = { x∈ℤ | x is an even number }



Empty Set symbol - correct answer ✔✔ Ø



Sample Space / Universal Set Symbol - correct answer ✔✔ Ω



How to denote complement - correct answer ✔✔ S^c



What Ω^c = - correct answer ✔✔ Ø



The union of sets S and T - correct answer ✔✔ - S or T (or both)

- S∪T = { x | x∈S or x∈T }



The intersection of sets S and T - correct answer ✔✔ - S and T

- S∩T = { x | x∈S and x∈T }