simulation example: generate a distribution for the random variate: what is the approximate...
Post on 04-Jan-2016
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Simulation
• Example: Generate a distribution for the random variate:
What is the approximate probability that you will draw X ≤ 1.5?
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HHHHMMMM…
SimulationWhat if we crank up the
sample sizes?
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SimulationHere is how we did all of that:
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So what was the mean of that original Weibull distribution anyway?
Looks like that’s where the mean on the histograms is going
SimulationHow about the variance and sd?
= 0.376sWeibull= 0.613
= 1.5a = 1b
So what did we observe?
Looks like the distribution of the sample means is a little skewed, but they’re approaching normal
So what did we observe?
So what did we observe?
• Generalizing to a IID sample, it can be shown that:
The Central Limit Theorem
For a sum of IID random variables
For an average of IID random variables
Example
Random errors in the response of an instrument’s detector occur according to some unknown distribution, but have a mean = 2.45 units and variance = 0.63 units2.
Approximately, what is the probability that the cumulative error is greater that 123 units after 50 measurements?
Plot the approximate probability density for the cumulative error after 73 measurements.
Simulation
A a certain stock price moves with the approximate behavior from month to month:• Pr(no change) = 0.5• Pr(up 5%) = 0.25• Pr(down 5%) = 0.25
Plot a realization of the stock’s movement assuming an initial stock price of $10.
Approximately how much money to you expect to make/loose after one year of owning the stock? Three years? Ten years?
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