a simple quesiton about probabityl

[yjj1119]

x=am+n(a is constant, m is random with pdf f(m), n is also a random with pfd f)
Then how to solve the pdf of f(m|x)

 

[timof]

x=am+n(a is constant, m is random with pdf f(m), n is also a random with pfd f)
Then how to solve the pdf of f(m|x)

The distribution function of the sum (am+n) is the convolution of f(am) and f.

See, for example:

https://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/Chapter7.pdf