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MAT136H1 Lecture Notes - Probability Distribution, Standard Deviation

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8.5 Challenging Integral Applications
Probability Applications: Overview
Random Variables
Continuous random variables: their values change over the interval
Any continuous random variable has its probability density function , so that the probability of
lying between a and b is given by: 
Usually  for all
Since probabilities are measured from to , 
Mean Value
Mean value of any probability density function: 
 
Exponential Distribution
This typically represents wait time, so that: 
Normal Distributions
The probability density function: 
, whose mean value is and the standard
deviation is
For small , the values of are centered around the mean
For large , the values of are spread out from the mean
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