How to express this as a joint probability density function?

How to express this as a joint probability density function?

References

Reference NO 1

http://stackoverflow.com/questions/15192183/how-to-express-this-as-a-joint-probability-density-function

Reference NO 2

http://en.wikipedia.org/wiki/Joint_probability_density_function

Reference NO 3

http://www.stat.lsu.edu/faculty/zzzdowner/4050notes/jointexamp.pdf

Reference NO 4

http://www.stat.duke.edu/courses/Fall05/sta104/hw/hw08sol.pdf

Reference NO 5

http://mathworld.wolfram.com/JointProbabilityDensityFunction.html

Reference NO 6

http://archives.evergreen.edu/webpages/curricular/2005-2006/maths/spring/solns/prob7.pdf

Reference NO 7

http://dss.ucsd.edu/~ssaiegh/Slides8.pdf

Reference NO 8

http://math.stackexchange.com/questions/344194/exponential-probability-density-functions-of-independent-variables