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The linear stochastic equation dxβ(t)/dt + [1 + fβ(t)]xβ(t) = Asin(Ωt) is discussed. The function fβ(t) is defined as a Poissonian noise dependent on a parameter β > 0, fβ = β∑j[δ(t−t+j−δ(t−t−j]. The mean frequency of the delta-pulses is chosen as β-dependent in the form λ(β) = 2γ(β−2 + 1)exp(−β) where γ is a constant from the interval (0, 0.974). With the stochastic function fβ(t) defined in this way, attention is paid on the oscillational term of the averaged function 〈x(t〉, 〈x(t)〉osc = Āsin(Ωt − α. It is found that the dependence Ā = Ā(β) exhibits one maximum and one minimum. The occurrence of these extrema seems to affirm the presence of stochastic resonance.