Apoptosis is a cell suicide mechanism that enables metazoans to control cell number in tissues and to eliminate individual cells that threaten the animal's survival. Dependent on the type of stimulus, apoptosis can be propagated by intrinsic pathway or extrinsic pathway. Previously, we have proposed a deterministic model of intrinsic apoptosis pathway which is bistable in a robust parameter region. Cellular networks, however, are inherently stochastic and significant cell-to-cell variability in apoptosis response has been observed at single cell level. In this work, we examine the impact of intrinsic stochastic fluctuations as well as variation of protein concentrations on behavior of the intrinsic apoptosis network. First, Gillespie Stochastic Simulation Algorithm (SSA) of the model is implemented to account for intrinsic noise. Using histograms of steady-state output at varying input levels, we show that the intrinsic noise in the apoptosis network elicits a wider region of bistability. We further analyze the dependence of system stochasticity due to intrinsic fluctuations, such as steady-state noise level and random response delay time, on the input signal. We find however that the intrinsic noise is insufficient to generate significant stochastic variations at physiologically relevant level of molecular numbers. Finally, extrinsic fluctuation represented by variations of two key proteins is modeled and the resultant stochasticity of apoptosis timing is analyzed. Indeed, these protein variations can induce cell-to-cell stochastic variability at a quantitative level agreeing with experiments. Therefore, we conclude that the heterogeneity in intrinsic apoptosis responses among individual cells plausibly arises from extrinsic rather than intrinsic origin of fluctuations.