统计学重点整理CH6-Continuous Probability Distributions
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CH6
Continuous distributions
Continuous distributions are constructed from continuous random variables in which values are
taken for
every point over a given interval
With continuous distributions, probabilities of outcomes occurring between particular points
are determined by calculating the area under the curve between these points
Uniform Distribution
The uniform distribution is a relatively simple continuous distribution in which the same height f(x), is obtained over a range of values
Mean and standard deviation of a uniform distribution
Mean μ = (a + b)/2
Std Dev σ = (b-a)/Square root 12
With discrete distributions, the probability function yields the value of the probability
For continuous distributions, probabilities are calculated by determining the area over an interval
of the function
Properties of the Normal Distribution
Characteristics of the normal distribution:
Continuous distribution - Line does not break
Symmetrical distribution - Each half is a mirror of the other half
Asymptotic to the horizontal axis - it does not touch the x axis and goes on forever
Unimodal - means the values mound up in only one portion of the graph
Area under the curve = 1 ; total of all probabilities = 1
Probability Density Function of the Normal Distribution
Standardized Normal Distribution
Z score can be used to find probabilities for any normal
curve problem that has been converted to Z scores
Z distribution is normal distribution with a mean of 0
and a Std Dev of 1
Exponential Distribution
Continuous
Family of distributions
Skewed to the right
X varies from 0 to infinity 0 ,0for )(XXfeX esother valu all01)(forbxaforabxf
12Deviation Standardab
. . . 2.71828 . . . 3.14159 =X ofdeviation standard X ofmean :21)(221eWherexxfe xz
Apex is always at X = 0
Steadily decreases as X gets larger
Probability function P(x)=x2−x1b−a
μ= 1λ
eXXXP00 σ= 1λ
