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# lecture3 - Statistics Tutorial(Part 1 of 2 The mark of a...

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Statistics Tutorial (Part 1 of 2) 1 Lecture #3: Statistics Tutorial (Part 1 of 2) The mark of a truly educated man is to be moved deeply by statistics. -- George Bernard Shaw (1856 – 1950) Irish playwright and winner of the Nobel Prize for Literature (1925)

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Dogbert’s risk management advice 2 Lecture #3: Statistics Tutorial (Part 1 of 2)
Dogbert’s risk management advice 3 Lecture #3: Statistics Tutorial (Part 1 of 2)

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Dogbert’s risk management advice 4 Lecture #3: Statistics Tutorial (Part 1 of 2)
(Just about) all the statistics you’ll need In this lecture. . . expected value, variance, standard deviation, covariance, correlation, and skewness discrete and continuous probability distributions 5 Lecture #3: Statistics Tutorial (Part 1 of 2)

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What is a Probability Distribution? First, we must define the concept of a probability distribution. A probability distribution is a mathematical function which defines the set of possible realized values for a random variable and the probability associated with each possible 6 Lecture #3: Statistics Tutorial (Part 1 of 2)
Discrete & Continuous Distributions There are two types of random variables: discrete and continuous. Consider the following examples: Discrete random variable: sizes of shoes worn by Baylor students. Continuous random variable: actual foot sizes of Baylor students. 7 Lecture #3: Statistics Tutorial (Part 1 of 2)

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Discrete Probability Distribution The mathematical definition of a discrete  probability function,  p s , is a function that satisfies  the following properties.   1. The probability that the random variable  X  can  take a specific state contingent value  X s  is  p ( X s );  that is, Pr[ ] ( ) . s s s X X p X p = = =   2. p s  is non-negative for all possible values of  X s 3. The sum of  p s  over all possible states is 1; i.e.,  1 1. n s s p = =   8 Lecture #3: Statistics Tutorial (Part 1 of 2)
Continuous Probability Distribution The mathematical definition of a continuous  probability function,  f ( x ), is a function that  satisfies the following properties.   1. The probability that  x  is between two  points  a  and  b  is  Pr[ ] ( ) . b a a x b f x dx =   2. f ( x ) is non-negative for all possible values  of  x .   3. The integral of the probability function is  one; that is,  ( ) 1. f x dx -∞ =   9 Lecture #3: Statistics Tutorial (Part 1 of 2)

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Lecture #3: Statistics Tutorial (Part 1 of 2) 10 Expected value Expected value is also known as the mean, or average value for a random variable. If you roll a die, there is an equal (1/6) probability of each number coming up (note: since all outcomes are equally probable, this is an example of a “uniform” probability distribution). What is the expected value or average
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lecture3 - Statistics Tutorial(Part 1 of 2 The mark of a...

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