Re: Questions about probability functions

In article <1148048324.775375.186130@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Zerex71 <mfeher@xxxxxxxxxxx> wrote:

1. In a standard distribution, what more is needed to characterize the
bell curve other than the mean and the standard deviation (sigma)? I
ask this because some of the modeling and analysis tools that I am
using seem only to need those two parameters to determine fragment
dispersions and flyouts.

The mean and standard deviation are the only two parameters for the
normal distribution. Of course, there are other distributions...

2. In plain English, what is the difference between a probability
density function (PDF) and a cumulative distribution function (CDF)? I
know one is the derivative of the other and so on, but what is the
physical significance of the two?

The CDF of a random variable X tells the probability that the random
variable is at most a given value, i.e. F(x) = Prob {X <= x}.

The PDF f(x) says that if you consider a small interval of values
near x, the probability that X is in that interval is approximately
f(x) times the length of the interval. Thus
f(x) is the limit of Prob{x <= X <= x + t}/t or
Prob{x - t <= X <= t}/t as t -> 0+.

3. In Monte Carlo simulation, isn't that basically just a random-number
generator being used for "draws" against a particular phenomenon, and
then comparing the draw to a scale or thermometer to determine the
outcome of the event in question?

I'm not sure what the question is. In the context of a random variable
arising in some process, the basic idea is to use a pseudo-random number
generator to simulate the process, generating a large sample from (if
you did it right) the distribution of the random variable. You
then study the sample to draw whatever conclusions you want about the
distribution of the random variable.

Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada

.

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