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To: cs551@merlot.usc.edu
Subject: Re: Exponential distribution calculation
Date: Sun, 10 Sep 2006 22:57:26 -0700
From: william@bourbon.usc.edu
Someone wrote:
> I'm little bit confused about the exponential distribution
> calculation. In the lecture notes it says,
> y = 1 - e^(-mx).
>
> What is the parameter y?
y is F(x). Usually, we plot F(x) on the vertical axis
and x on the horizontal axis. The vertical axis is
also known as the y-axis and the horizontal axis is
also known as the x-axis.
> I'm confused about calculating the w
> given lamda or mu. Could you please illustrate the steps?
r is an instance of y, to get w, you need F^{-1}(x), the
inverse of F(x). To get F^{-1}(x) is easy since we have
the equation for F(x):
y = 1 - e^(-mx)
e^(-mx) = 1 - y
-mx = ln( 1 - y )
x = (-1/m) ln( 1 - y )
Therefore,
w = F^{-1}(r) = (-1/m) ln( 1 - r )
and m is either lambda or mu. I think I did the above
correctly, but you should make sure what you get is
correct (including the units).
--
Bill Cheng // bill.cheng@usc.edu