Density of continuous random variables?

AI Thread Summary
The density function for the continuous random variable X is defined piecewise for the intervals 1<x<2 and 2<x<3. To find the density of Y, where Y = 4X-2, the transformation of variables method can be applied, adjusting the density accordingly. For M, defined as M = (X-2)^2, the density can be derived using the change of variables technique, considering the range of X. The discussion emphasizes the importance of posting such questions in the appropriate forum section for better assistance. Properly detailing attempts to solve the problem is also encouraged for effective guidance.
icup007
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Can you please help me find the density of the following functions?

The density of an absolutely continuous random variable X is:

fX(x) =
{ (3x^2-1)/12 if 1<x<2
{ 1/2 if 2<x<3
{ 0 elsewhere

Find the density of Y where Y = 4X-2
Find the density of M where M = (X-2)^2


Thank you!
 
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