How do i find confidence interval for $P(a<X<b)$, with $a,b$ known and $X\sim \text{Exp}(\theta)\,$? $(x_1,x_2,…,x_n)$ are given, where the $x_i$ are iid exponential random variables.
My initial idea was to find $$P(a<X<b)=P(X<b)-P(X<a)=e^{-\theta a}-e^{-\theta b}$$ and then isolate $\theta$, so i can transform the usual confidence interval for $\theta$.