概率论教案(全英)
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probability…
*Whaaat???!! Yes. If E2 and E1 have no influence on each other it will
be this simple.
Basic Probability Rules
• Complement P(X E1) 1 P(E1)
• And
P( X E1 E2 ) P( X E1) P( X E2 ) P( X E1 E2 )
• And E1 E2 is when E1 and E2 both occur
E1 E2
E1 E2
COMBINING EVENTS
Combinations of Events
Probability of happening is the complement of it not happening…
– E.g. P(error=-0.225)
• A discrete variable takes a specific value
– E.g. P(count=3)
• One of a finite number of outcomes occurs
– E.g. P(fault=‘gearbox failure’)
• Previous example demonstrates events form part of a set
• Set theory is applicable then • What was set theory again?
– You may remember it, but in case you don’t… – …quick review and how it relates to
interpreted as relative frequency • A probability is usually expressed in terms of a random variable.
• In this example, X denotes the part length and the probability statement can be written as :
EE313/EM301Engineering Analysis Lesson 2a: Basic Probability (Events)
Probability
• Probability is used to quantify the likelihood that a measurement falls within some set of values
frequency interpretation is still appropriate
• E.g. outcome X from rolling a dice
• 6 outcomes; P(X=1)=1/6 ; P( X [1,6]) 1
Types of Events
• A continuous variable takes a specific value:
P(X [10.8,11.2]) 0.25 or P(10.8 X 11.2) 0.25
Events
• A measured value is not always obtained from an experiment. Sometimes, the result is only classified into one of several categories.
• The possible categories are referred to as outcomes • A set of one or more outcomes is called an event. • The concept of probability can be applied to events and the relative
• Irrespective, P is still a real value
Types of Events
• Mutually exclusive events (e.g. E1=‘Guilty’ E2=‘Not Guilty’):
• If two events, E1 and E2, are mutually exclusive, they have no common sample points in X
• And P( X E1 E2 ) P( X E1) P( X E2 )
E1
E2
• Non-mutually exclusive events (e.g. E1=‘EEE’ E2=‘MAE’):
• Two events, E1 and E2, are not mutually exclusive when they have one or more common sample points
• The following statement:
“The chance that X, the lifetime of a power transformer, iБайду номын сангаас between 10.8 and 11.2yrs is 25%”
is a statement that quantifies the possibility of plant lifetime • The value of a probability is always restricted to the interval [0,1] and can be
• For example, a manufactured electronic component might only be classified as defective or not – 2 categories.
• For example, a circuit breaker with fail if just one of its 15 subassemblies fails – the cause will be one of 15 categories.
*Whaaat???!! Yes. If E2 and E1 have no influence on each other it will
be this simple.
Basic Probability Rules
• Complement P(X E1) 1 P(E1)
• And
P( X E1 E2 ) P( X E1) P( X E2 ) P( X E1 E2 )
• And E1 E2 is when E1 and E2 both occur
E1 E2
E1 E2
COMBINING EVENTS
Combinations of Events
Probability of happening is the complement of it not happening…
– E.g. P(error=-0.225)
• A discrete variable takes a specific value
– E.g. P(count=3)
• One of a finite number of outcomes occurs
– E.g. P(fault=‘gearbox failure’)
• Previous example demonstrates events form part of a set
• Set theory is applicable then • What was set theory again?
– You may remember it, but in case you don’t… – …quick review and how it relates to
interpreted as relative frequency • A probability is usually expressed in terms of a random variable.
• In this example, X denotes the part length and the probability statement can be written as :
EE313/EM301Engineering Analysis Lesson 2a: Basic Probability (Events)
Probability
• Probability is used to quantify the likelihood that a measurement falls within some set of values
frequency interpretation is still appropriate
• E.g. outcome X from rolling a dice
• 6 outcomes; P(X=1)=1/6 ; P( X [1,6]) 1
Types of Events
• A continuous variable takes a specific value:
P(X [10.8,11.2]) 0.25 or P(10.8 X 11.2) 0.25
Events
• A measured value is not always obtained from an experiment. Sometimes, the result is only classified into one of several categories.
• The possible categories are referred to as outcomes • A set of one or more outcomes is called an event. • The concept of probability can be applied to events and the relative
• Irrespective, P is still a real value
Types of Events
• Mutually exclusive events (e.g. E1=‘Guilty’ E2=‘Not Guilty’):
• If two events, E1 and E2, are mutually exclusive, they have no common sample points in X
• And P( X E1 E2 ) P( X E1) P( X E2 )
E1
E2
• Non-mutually exclusive events (e.g. E1=‘EEE’ E2=‘MAE’):
• Two events, E1 and E2, are not mutually exclusive when they have one or more common sample points
• The following statement:
“The chance that X, the lifetime of a power transformer, iБайду номын сангаас between 10.8 and 11.2yrs is 25%”
is a statement that quantifies the possibility of plant lifetime • The value of a probability is always restricted to the interval [0,1] and can be
• For example, a manufactured electronic component might only be classified as defective or not – 2 categories.
• For example, a circuit breaker with fail if just one of its 15 subassemblies fails – the cause will be one of 15 categories.