  For the Dirichlet series of the form $\displaystyle
F(z,\omega)=\sum\nolimits_{k=0}^{+\infty} f_k(\omega)e^{z\lambda_k(\omega)} $ $
(z\in\mathbb{C},$ $\omega\in\Omega)$ with pairwise independent real exponents
$(\lambda_k(\omega))$ on probability space $(\Omega,\mathcal{A},P)$ an
estimates of abscissas convergence and absolutely convergence are established.
