Uniform Distribution and Transformations

May 2010
6
0
Hi, I have a question regarding the uniform distribution and it's respective joint density, cdf and pdf, along with transformations. In essence, these are three questions in one.

Since I am truly an amateur at using the online LaTeX math tool and because I do not want to make any errors, I am simply going to attach a jpg of the question which features from a set of practice questions assigned to us at University.



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Help is much appreciated.
 
Nov 2009
517
130
Big Red, NY
Hi, I have a question regarding the uniform distribution and it's respective joint density, cdf and pdf, along with transformations. In essence, these are three questions in one.

Since I am truly an amateur at using the online LaTeX math tool and because I do not want to make any errors, I am simply going to attach a jpg of the question which features from a set of practice questions assigned to us at University.



-----

Help is much appreciated.
Where are you stuck, particularly?

Stuff:

(a) They are independent so you can multiply the two uniform densities to find the joint density... I assume you know the density for U(0,1).

(b) ...Do the integration. Figure out your bounds by inspecting [0,1]/[0,1]. You may have some questions about bounds.

(c) You have the formula in your notes... Post any questions about transforming/computing Jacobian...etc.
 
May 2010
6
0
Where are you stuck, particularly?

Stuff:

(a) They are independent so you can multiply the two uniform densities to find the joint density... I assume you know the density for U(0,1).

(b) ...Do the integration. Figure out your bounds by inspecting [0,1]/[0,1]. You may have some questions about bounds.

(c) You have the formula in your notes... Post any questions about transforming/computing Jacobian...etc.
For part (a), I reached upon the solution t1 x t2. Is this correct?

I really tried going through my notes, but sadly my statistical analysis is really quite poor, so I really don't even know how to go about with case (b).

Perhaps you could help me with (b), and I could thereafter attempt (c) and get back to you?

Thanks ever so much.