Probability and Statistics
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Probability is measured
between 0 and 1

Probability =
 # of Ways A could happen
 Total # of Outcomes

Misconceptions about Probability
 It is the likelihood of an event, not a certainty
 Past outcomes do not influence future outcomes
 There is no such thing as an event being "due"

Discrete Probability Distributions have how many possible outcomes?
a limited, distinct number

Coefficient of Variation
 Standard Deviation
 Expected Value

Cumulative Distributions (CDFs)
Probability that the outcome is Less Than or Equal to some value for all possible values


2 Types of Exceedance Probability Curves:
 Occurrence  largest loss within a year
 Aggregate  sum of all losses within a year

2 Ways to express Probabilities:
 Return Periods, or
 Exceedance Probabilities (EP)
They are the same thing. We prefer EPs. A 1% probability correlates to a 100 year return period. (1 in 100 chance, or 1%)

Tail Value at Risk (TVAR)
%TVAR is the average loss of all years with having an EP<p.
.1% TVAR is the expected losses given the EP<.1%.

Numerical Convolution
Combines the probability distributions of two events into a single probability distribution that represents the sum of the two events.
Touchstone uses this to combine loss distributions.