Thanks to BGM and Dragan, my problem posted under the thread " A question about the distribution of random numbers" now appears to be solved! The solution is:
![f_C(a) =
\Phi\left(\frac {\mu_A - \mu_B} {\sqrt{\sigma^2_A + \sigma^2_B}}\right)^{-1}
\Phi\left(\frac {a - \mu_B} {\sigma_B}\right)\frac {1} {\sigma_A}\phi\left(\frac {a - \mu_A} {\sigma_A}\right)]( "f_C(a) =
\Phi\left(\frac {\mu_A - \mu_B} {\sqrt{\sigma^2_A + \sigma^2_B}}\right)^{-1}
\Phi\left(\frac {a - \mu_B} {\sigma_B}\right)\frac {1} {\sigma_A}\phi\left(\frac {a - \mu_A} {\sigma_A}\right)")
I do have an interesting continuation to the problem, however:
The solution above shows the distribution of random variable C. My question is, given any value of C, what is the expected value of A?
I do have an interesting continuation to the problem, however:
The solution above shows the distribution of random variable C. My question is, given any value of C, what is the expected value of A?