# Random Variable Transformation

Consider a Probability density function f(x) which is uniformly distributed between say (-5,5).Now if i define a random variable "y" which is related to the random variable "x" as follows:

y = 1 ; -2.5 < x < 2.5. (zero outside)

Since this mapping neither one to one nor does it correspond to a monotonic function.

How can i find the probability density function of transformed random variable?

• Our site offers a wealth of worked examples and techniques for solving such problems. Why not search it? One of the higher-voted threads that turns up looks like it fully answers your question: see stats.stackexchange.com/questions/144138. Please note that your example is not appropriate for your question, because $Y$ will not have a PDF at all. – whuber Jan 13 '16 at 0:28