Suppose that if a signal value $s$ is sent from location $A$ ,then the signal value received at location $B$ is normally distributed with parameters $(s,1)$.Let $S$,the value of the signal sent at A,be normally distributed with parameters $(\mu,\sigma)$and $R$ be the value received at $B$ Derive the joint$p.d.f$.
I only know can use
$f_{S|R}*f_{R}$
$f_{R|S}*f_{S}$
to solve the question
But don't know which is condition?
I am confused the condition is S or R?
Your received signal $R$ is distributed as $\mathcal N(S,1)$, while your transmitted signal value is distributed as $\mathcal N(\mu,\sigma^2)$. So the distribution of the received signal depends on the transmitted value. You can therefore condition the distribution of $R$ on $S$ and use: $$f_{S,R} = f_{R|S}(r|s)f_S(s)$$