I have this confusion related to calculating the probability distribution of a variable. If I have a variable $x_1$ which has a pdf $p(x_1)$.Lets assume that the distribution is gaussian with mean $X_1$. I sample a point from this distribution lets say $X_1'$.
Now I have another random variable $x_2$ which has a distribution $p(x_2)$. Its mean is equal to a constant, $X_2$ plus the previous sample $X_1'$. So how can I write the pdf function for this random variable $x_2$. I mean I want its mean to be dependent upon the sample from the distribution of $x_1$.