I want to find the Mean and variance of one random variable having a reciprocal truncated exponential distribution function over the interval [a,b]
I used the following code (n=1)
n=1;
ExpDist = ExponentialDistribution[\[Lambda]];
TruDist = TruncatedDistribution[{1/b, 1/a}, ExpDist];
OrdDist = OrderDistribution[{TruDist, n}, n];
FullSimplify [Mean[OrdDist], Assumptions -> {b > a && a > 0, \[Lambda] > 0}]
FullSimplify [Moment[OrdDist, 2] - Power[Mean[OrdDist], 2],
Assumptions -> {b > a && a > 0, \[Lambda] > 0}]
I got wrong result. Any help please