Related post: Distribution of median of three exponential observations
However, Suppose $Y=Median(X_1,X_2,X_3)$ where $X_1,X_2,X_3$ are unordered, i.e. $X_1>X_2$ or $X_1<X_2$ are all possible, independent exponential distribution with paramater $\theta$.
What's the pdf for $Y$?