Probability and Statistics
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Probability is measured
between 0 and 1
- # 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%.
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.
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