Start at a point (0,1) in a rectangular coordinate system, choose an angle and draw the line to cross the x-axis at X. The range for X is . Find the pdf of X.

I picked the angle and now have no idea what to do.

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- April 9th 2011, 04:11 PMdwsmithFind PDF
Start at a point (0,1) in a rectangular coordinate system, choose an angle and draw the line to cross the x-axis at X. The range for X is . Find the pdf of X.

I picked the angle and now have no idea what to do. - April 9th 2011, 07:40 PMTKHunny
What an odd question. Anyway, you do not seem to have a useful idea. Let's see if I can make some sense of it...

I believe the intent is to choose ANY angle, not a specific one, but ALL of them in the given range. Perhaps examples would be useful.

P(X<0) = 1/2 and this corresponds to

P(X<-1) = 1/4 and this corresponds to

P(X<1) = 3/4 and this corresponds to

Essentially, what I am trying to define is a mapping from a uniform distribution on [-pi/2,pi/2] to the entire x-axis. Sounds like it might be related to a tangent, perhaps. - April 9th 2011, 08:15 PMSambit
http://img163.imageshack.us/img163/2677/unledvf.png

It reduces to the pdf of a**standard Cauchy**distribution. Angle OQP is in the figure and OP=x.

The pdf of can be written as: , when .

Also, . Then the cdf of X can be given by:

, , where is the cdf of

So the pdf of X is given by:

, where is the pdf of

=

= which is a Standard Cauchy pdf.