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For a bivariate random variable $(Z_1,Z_2)$ having Kulkarni's bivariatephase-type distribution (see \cite{Ku89}), we derive a simple expression forthe semi-explicit density function $E (e^{-sZ_2} 1_{ \{ Z_1 \in dy \} })$. Someimmediate consequences are presented as concluding remarks.

A semi-explicit density function for Kulkarni's bivariate phase-type distribution