Applied Probability I Notes
Assessment:
Exam 2 hours (80%)
Compulsory group project (20%, 3-4 people)
Examinable: All material presented in class unless described otherwise
Uncertainty
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Weather forecasting:
Initial physical conditions are uncertain, goal is to predict future weather based on
current and past conditions
Initial physical conditions are uncertain
Probabilistic model to deal with uncertainty
Uncertainty is taken into account by choosing, at random, the initial conditions of the physical system
Many replicates of the same random experiment – Summary of the outcomes will tell us about the
system’s evolution. Uncertainty must be reported
Solving the Birthday Problem
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Assign at random a birthday to each of the 23 people on the field
Check whether there is at least a repetition among the 23 birthdays
Count this experiment as a ‘fail’ if there is at least one repetition
Repeat the experiment several times and compute the relative frequency of fails
P = # fails / # experiment
P(AK) = 1 ( 1 – 1/365) * 1 (1 – 2 / 365) … (1 – k-1 / 365)
There is an equal chance that both people have the same birthday
After running 10000 experiments, we get p = 0.505
This type of simulation is known as a monte carlo simulation