# Why isn't that conditional expectation calculated directly?

I mean

Expectation[y \[Conditioned]  x/y == t, {x \[Distributed] ExponentialDistribution[2],
y \[Distributed] ExponentialDistribution[3]}]


returns the input in 13.2 on Windows 10. That expectation can be calculated as follows.

Expectation[y \[Conditioned]  x/y <= t + eps && x/y >= t - eps,
{x \[Distributed]  ExponentialDistribution[2],  y \[Distributed] ExponentialDistribution[3]}]


Piecewise[{{(2*(3 + eps + t))/(9 + 6*eps + 6*t), eps >= t && eps > 0 && eps + t > 0}, {(6 + 4*t)/(-4*eps^2 + (3 + 2*t)^2), eps < t && eps > 0}}, 0]

Limit[%, eps -> 0, Direction -> "FromAbove"]


Piecewise[{{2/(3 + 2*t), t >= 0}}, 0]

I am not able to trace the command under consideration to find out the reason. It would be kind of more experienced users to explain such a behavior.

• The same issue with Expectation[ y \[Conditioned] x + y == t, {x \[Distributed] ExponentialDistribution[2], y \[Distributed] ExponentialDistribution[3]}] and Expectation[ y \[Conditioned] x * y == t, {x \[Distributed] ExponentialDistribution[2], y \[Distributed] ExponentialDistribution[3]}] Feb 24 at 16:19