{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# APME_1 - Click to edit Master subtitle style Applied...

This preview shows pages 1–18. Sign up to view the full content.

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

View Full Document

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

View Full Document

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

View Full Document

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

View Full Document

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

View Full Document

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

View Full Document

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

View Full Document

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

View Full Document

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.

Unformatted text preview: Click to edit Master subtitle style Applied Probability Methods for Engineers Slide Set 1 Click to edit Master subtitle style Chapter 1 Probability Theory Probability and Statistics n How would we define the word probability ? n Likelihood, relative frequency, chance n How would we define the word statistic ? n A property or measure associated with a sample taken from a population, typically used to make inferences about the population n Probability and statistics tools have been developed to help us deal with things we do not or can not know with certainty Introductory Probability Theory n Experiment: process that can lead to more than one outcome n Sample Space: Set of all possible outcomes associated with an experiment n Sample Space for picking a card from a deck: Introductory Probability Theory n Sample space for choosing two cards with replacement: Introductory Probability Theory n Sample space for choosing two cards without replacement: Probability Values n Given a sample space S consisting of n outcomes { O 1, O 2, ..., On }, a set of n probability values satisfies: n 0 ≤ p 1 ≤ 1, 0 ≤ p 2 ≤ 1, …, 0 ≤ pn ≤ 1, and n p 1 + p 2 + … + pn = 1 n The probability of outcome Oi occurring is pi , and we write this as P( Oi ) = pi Probability Values n Associated with picking a single card: Probability Values n Associated with picking two cards with replacement Probability Values n Associated with picking two cards without replacement: Events/Complements n An event A is a subset of sample space S, and the event A occurs if one of the outcomes contained in the event occurs n P(A) denotes the probability of event A, and is obtained by summing probabilities of the outcomes associated with the event n P(A) = 0.10 + 0.15 + 0.30 = 0.55 Events/Complements n The event A' is everything not contained in A, and is called the complement of A n P(A') = 0.10 + 0.05 + 0.05 + 0.15 + 0.10 = 0.45 = 1 – P(A) Event Examples n Probability a randomly drawn cards belongs to hearts suit (event A) n P(A) = 13*(1/52) = 13/52 = 1/4 Event Examples n Probability a randomly selected card is a picture card (event B) n P(B) = 12*(1/52) =12/52 = 3/13 Event Combinations n Intersection of events A and B, denoted A ∩ B, consists of all outcomes in both A and B n P(A ∩ B) is the probability both A and B occur at the same time n Clearly P(A ∩ A') = P(& ) = 0 n P(A ∩ B) + P(A ∩ B') = P(A) n P(A ∩ B) + P(A' ∩ B) = P(B) n Events A and B are mutually exclusive if they have no common outcomes n In this case A ∩ B = & and P(A ∩ B) = 0 Event Unions n The union of two events A and B, denoted by A ‚ B, consists of all outcomes either in A or B or both n P(A “ B) is the probability that at least one of the events A, B occurs n P(A & B) = P(A ∩ B') + P(A' ∩ B) + P(A ∩ B) n P(A ∩ B') = P(A) – P(A ∩ B) and n P(A' ∩ B) = P(B) – P(A ∩ B), implying n P(A & B) = P(A) + P(B) – P(A ∩ B) n When A and B are mutually exclusive, then P(A ∩ B) = = and we have P(A & B) = P(A) + P(B) (A and (not B)) or ((not A) and B) or (A and B both) Intersection Example n Probability a randomly selected card is a face card and hearts suit (= 3/52) Union Example...
View Full Document

{[ snackBarMessage ]}

### Page1 / 127

APME_1 - Click to edit Master subtitle style Applied...

This preview shows document pages 1 - 18. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online