Statistiek module PAP
Chapter 5 Probability Distributions (herhaling)
Probability distribution
- Expected value
- Standard deviation
Random Variable = represents a possible numerical value from an uncertain event
Discrete random Variable can only assume a countable number of values
- Roll a dice or toss a coin 5 times
Standard deviation of variable σ
σ = square root of [Sum of ( Squared differences between a value and the mean) x
( Probability of the value )]
VB σ (0 1)2 (0.25) (1 1)2 (0.50) (2 1)2 (0.25) 0.50 0.707
Mean = Sum of [ Each value x the probability of each value]
Binomial Probability Distribution
2 possibilities
- n = a fixed number of observations
- 2 mutually exclusive and collectively exhaustive
categories
o Generally called “success” and “failure”
o probability of success = P
o probability of failure = 1 - P
- Constant probability for each
Observation
- Observations are independent
o The outcome of one observation does not affect the outcome of
the other
2 sampling methods:
o Infinite population without replacement
o Finite population with replacement
The shape of the binomial distribution depends on the
values of p and n
1
, Poisson Probability Distribution: (Waiting Lines)
Hele getallen, minder dan 30 stuks, “area of opportunity”
- Apply this when:
o You wish to count the number of times an event occurs in a given area of
opportunity
o The probability that an event occurs in 1 area of opportunity is the same for all
areas of opportunity
o The number of events that occur in1 area of opportunity is independent of the
number of events that occur in the other areas of opportunity
o The probability that 2 or more events occur in an area of opportunity
approaches 0 as the area of opportunity becomes smaller
λ= The average number of events per unit
Continuous Probability
Distribution
- Continuous random variable = variable
that can assume any value on a continuum (can assume an uncountable number of
values)
o Thickness of an item
o Time required to complete a task
o Temperature of a solution
o Height, in inches
- These can potentially take on any value depending only on the ability to measure
accurately
Normal Distribution (alle andere getallen)
Changing μ shifts the distribution left or right
Changing σ increases or decreases the spread
The Standardized Normal:
- Any normal distribution (with any mean and standard deviation combination) can
be transformed into the standardized normal distribution (Z)
- Need to transform X units into Z units
The Z distribution always has a mean = 0 and standard deviation =1
2
Chapter 5 Probability Distributions (herhaling)
Probability distribution
- Expected value
- Standard deviation
Random Variable = represents a possible numerical value from an uncertain event
Discrete random Variable can only assume a countable number of values
- Roll a dice or toss a coin 5 times
Standard deviation of variable σ
σ = square root of [Sum of ( Squared differences between a value and the mean) x
( Probability of the value )]
VB σ (0 1)2 (0.25) (1 1)2 (0.50) (2 1)2 (0.25) 0.50 0.707
Mean = Sum of [ Each value x the probability of each value]
Binomial Probability Distribution
2 possibilities
- n = a fixed number of observations
- 2 mutually exclusive and collectively exhaustive
categories
o Generally called “success” and “failure”
o probability of success = P
o probability of failure = 1 - P
- Constant probability for each
Observation
- Observations are independent
o The outcome of one observation does not affect the outcome of
the other
2 sampling methods:
o Infinite population without replacement
o Finite population with replacement
The shape of the binomial distribution depends on the
values of p and n
1
, Poisson Probability Distribution: (Waiting Lines)
Hele getallen, minder dan 30 stuks, “area of opportunity”
- Apply this when:
o You wish to count the number of times an event occurs in a given area of
opportunity
o The probability that an event occurs in 1 area of opportunity is the same for all
areas of opportunity
o The number of events that occur in1 area of opportunity is independent of the
number of events that occur in the other areas of opportunity
o The probability that 2 or more events occur in an area of opportunity
approaches 0 as the area of opportunity becomes smaller
λ= The average number of events per unit
Continuous Probability
Distribution
- Continuous random variable = variable
that can assume any value on a continuum (can assume an uncountable number of
values)
o Thickness of an item
o Time required to complete a task
o Temperature of a solution
o Height, in inches
- These can potentially take on any value depending only on the ability to measure
accurately
Normal Distribution (alle andere getallen)
Changing μ shifts the distribution left or right
Changing σ increases or decreases the spread
The Standardized Normal:
- Any normal distribution (with any mean and standard deviation combination) can
be transformed into the standardized normal distribution (Z)
- Need to transform X units into Z units
The Z distribution always has a mean = 0 and standard deviation =1
2
