It has been reported that a carbon nanotube (CNT) is one of the strongest materials with its high failure stress and strain. Moreover, the nanotube has many favorable features, such as high toughness, great flexibility, low density, and so on. This discovery has opened new opportunities in various engineering applications, for example, a nanocomposite material design. However, recent studies have found a substantial discrepancy between computational and experimental material property predictions, in part due to defects in the fabricated nanotubes. It is found that the nanotubes are highly defective in many different formations (e.g., vacancy, dislocation, chemical, and topological defects). Recent parametric studies with vacancy defects have found that the vacancy defects substantially affect mechanical properties of the nanotubes. Given random existence of the nanotube defects, the material properties of the nanotubes can be better understood through statistical modeling of the defects. This paper presents predictive CNT models, which enable to estimate mechanical properties of the CNTs and the nanocomposites under various sources of uncertainties. As the first step, the density and location of vacancy defects will be randomly modeled to predict mechanical properties. It has been reported that the eigenvector dimension reduction (EDR) method performs probability analysis efficiently and accurately. In this paper, molecular dynamics (MD) simulation with a modified Morse potential model is integrated with the EDR method to predict the mechanical properties of the CNTs. To demonstrate the feasibility of the predicted model, probabilistic behavior of mechanical properties (e.g., failure stress, failure strain, and toughness) is compared with the precedent experiment results.