I have this confusion related to calculating the probability distribution of a variable. If I have a variable x1 which has a pdf p(x1).Lets assume that the distribution is gaussian with mean X1. I sample a point from this distribution lets say X1'.
Now I have another random variable x2 which has a distribution p(x2). Its mean is equal to a constant,X2 + the previous sample X1'. So how can I write the pdf function for this random variable x2. I mean I want its mean to be dependent upon the sample from the distribution of x1.