{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

132B_1_Recitation1_Probability_Review

132B_1_Recitation1_Probability_Review - EE132B Recitation 1...

This preview shows pages 1–6. Sign up to view the full content.

EE132B - Recitation 1 Probability review Prof. Izhak Rubin [email protected] Electrical Engineering Department UCLA 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Probability space • A probability space is defined by three parameters (V, E, P). – V: represents the sample space . • Sample space : the set of all the outcomes w. – E: represents the collection of subsets of V called events . An event is a set of outcomes. The set of events is E. – P: is a function of V that maps events to the interval [0, 1], i.e., P assigns probabilities to different events in E. 2
Random variable • Definition: A random variable X is a function that associates a real number with each elements of the sample space, i.e., (in more technical terms,) maps V R , or, assigns a value X(w) = R to each outcome w. 3

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example: Toss a coin V = {H, T} E = all possible combinations of V = {font, (H), (T), (H,T)} P: P(font) = 0 P(H) = ½ P(T) = ½ P(H, T) = 1 • An example of a random variable can be: X(H) = +1 (if you get a head, you win one dollar) X(T) = -1 (if you get a tail, you lose one dollar) 4
Three axioms of probability • Any probability function must obey the following: – 1. P(A) >= 0 – 2. P(AUB) = P(A) + P(B) iff A and B are disjoint – 3. P(V)=1 5

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 15

132B_1_Recitation1_Probability_Review - EE132B Recitation 1...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online