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Final

# Final Exam Review

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University of Guelph

Economics

ECON 2740

David Prescott

Winter

Description

Key Equations and Concepts
Random Discrete Variable- the random variable ▯ can taken any of a finite number of different
values (for example, a six sided die)
Random Continuous Variable- the random variable ▯ can take any of an infinite number of
numerical values
Variance- the average squared deviation of ▯ from its mean
▯ ▯
▯ ▯▯▯▯▯▯▯
▯ ▯ ▯ ▯▯ ▯▯▯ ▯ ·▯▯▯ ▯
▯ ▯
Standard Deviation- the average deviation of ▯ from its mean (also the squared variance)
▯▯▯ ▯▯▯ ▯
▯▯▯
σ▯ ▯ ▯▯
Coefficient Variation - a unit free measure that can be used to compare to things
▯▯ ▯▯ ▯
▯▯▯▯
Sample Quartiles- quartiles divide data into for equal parts, or quartiles
- ▯ ▯second quartile) is also the median
- The position of the first quartil▯ is found using the first equation, and the vale by the
▯
second equation
▯ ▯ ▯▯ ▯ 1▯▯
▯ 4
▯ ▯ 0.75▯ ▯ 0.25▯
▯ ▯ ▯
- The position of the third quartile is found usingthe first equation, and the vale by the
▯
second equation
▯ ▯ ▯▯▯1 ▯ ·3▯
▯ 4
▯ ▯ 0.25▯ ▯▯.75▯ ▯
Sample Median- the value that lies in the middle of the data set, and the position can be found
using the first equation, and the value using the second equation
▯▯ ▯ 1▯▯
▯▯▯ 2
▯▯▯05.▯ ▯ ▯0.5▯ ▯ Interquartile Range- the interquartile range contains the middle 50% of ordered observations, or
the values in between the first and third quartiles
▯▯ ▯ ▯ ▯▯
▯ ▯
Moments- there are four moments is statistics, summarized in the following table
Momen t Associated Statistics
First Mean
Second Variance
Third Skew
Fourth Kurtosis
Set- a set is a collection of objects, and subsets are contained in the set
Compliment- denoted ▯ or ▯ , it contains all the elements not in ▯
Union- denoted ▯ ∪▯ , is every element contained in both ▯ and ▯
- Note ▯ ∪▯ ▯ ▯ ∩▯ and are all the elements not in ▯ and ▯, so the unshaded area in the
following diagram
- ▯▯▯▯∪▯ ▯▯ ▯▯ ▯▯ ▯▯ ▯▯ ▯ ▯▯▯▯ ▯ ∩▯ ▯▯
Intersection- denoted ▯ ∩▯ , is the set of elements in both ▯ and ▯ Mutually Exclusive- two subsets are mutually exclusive if their intersection is empty, so ▯ ∩▯▯0
Collectively Exhaustive- every element in ▯ is in at least on of ▯,▯ or ▯, so ▯ ∪▯∪▯▯▯
Partition- every element of ▯ is in one of the subsets that defines the partition and no element is in
more than on subset
Conditional Probability- the probability of event ▯, given that event ▯ has occurred
▯ | ▯ ▯▯▯ ∩▯▯
▯ ▯ ▯ ▯ ▯▯▯▯▯▯▯▯
Statistical Independence- if the occurrence or non-occurrence of ▯ does not change the
probability of ▯, thand ▯ and ▯ are statistically independent
▯ ▯ ▯ ▯▯ ▯ ▯ ▯
▯ ▯ ▯ ▯▯ ▯ ▯ ▯
▯ ▯ ∩▯ ▯ ▯▯ ▯ ·▯ ▯▯ ▯
Symmetry- if the mean and median are equal, the distribution is symmetric, but if the mean and
median are not equal we cannot say the distribution is not symmetric
Co-Variance- the average of the product of deviations
- Does not measure how close the data points are to the major axis
▯▯▯ ▯,▯ ▯ 1▯▯ ▯ ▯▯▯▯▯̅▯▯▯▯▯▯▯▯
Major Axis- the slope is the ration of the two standard deviations ▯ and ▯
Correlation Coefficient- measures how close the data points are to the major axis
- It is also unit free

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