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##### Overview:

Statistics and mathematics underlie the theories of finance. Probability Theory and various distribution types are important to understanding finance. Risk management, for instance, depends on tools such as variance, standard deviation, correlation, and regression analysis. Financial analysis methods such as present values and valuing streams of payments are fundamental to understanding the time value of money and have been in practice for centuries.

Probability P, 0<P<1
• Multiplication rule for independent events: Prob(A and B) = Prob(A)*Prob(B)
• Probability of n independent accidents = P^n
• Probability of x accidents in n policies (Binomial Distributon):

Expected Value, Mean, Average

Variance and Standard Deviation

• Variance (^2)is a measure of dispersion
• Standard deviation is square root of variance

Covariance
• A Measure of how much two variables move together

Correlation
• A scaled measure of how much two variables move together

Present Discounted Value (PDV)
• PDV of a dollar in one year = 1/(1+r)
• PDV of a dollar in n years = 1/(1+r)^n
• PDV of a stream of payments x1,..,xn

Consol and Annuity Formulas
• Consol pays constant quantity x forever
• Growing consol pays x(1+g)^(t-1) in t
• Annuity pays x from time 1 to T