The tripartite synapse denotes the junction of a pre- and postsynaptic neuron modulated by a synaptic astrocyte. Enhanced transmission probability and frequency of the postsynaptic current-events are among the significant effects of the astrocyte on the synapse as experimentally characterized by several groups. In this paper we provide a mathematical framework for the relevant synaptic interactions between neurons and astrocytes that can account quantitatively for both the astrocytic effects on the synaptic transmission and the spontaneous postsynaptic events. Inferred from experiments, the model assumes that glutamate released by the astrocytes in response to synaptic activity regulates store-operated calcium in the presynaptic terminal. This source of calcium is distinct from voltage-gated calcium influx and accounts for the long timescale of facilitation at the synapse seen in correlation with calcium activity in the astrocytes. Our model predicts the inter-event interval distribution of spontaneous current activity mediated by a synaptic astrocyte and provides an additional insight into a novel mechanism for plasticity in which a low fidelity synapse gets transformed into a high fidelity synapse via astrocytic coupling.