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Rock characterizations play an important role in designing rock engineering, mining, geotechnical, and other infrastructure projects. Uniaxial compressive strength (UCS) and Young’s modulus (E) are important parameters while forecasting a variety of issues encountered during various rock engineering projects. However, the determination of these properties of rocks in the laboratory test are tedious, time-consuming, expensive, and depends upon the availability of testing machines. Several efforts have been made by the researchers to evaluate and correlate these properties. However, this is the first study to incorporate the thermal coefficient of conductivity of hard rocks during the deterministic and stochastic modelling of UCS and E of various rock sample. In this study, an attempt has been made to predict the UCS and E of intact rocks by multiple linear regression (MLR), artificial neural network (ANN) and Monte Carlo Simulation (MCS) beyond conventional practices. An excellent database always needs high-quality data closely resembling real-world problems. A total of 153 datasets of hard rocks were compiled in this study. A deterministic model has been established in the study in order to determine the UCS and E of various intact rocks. To train the model, different rock characterizations properties including wave velocity (Vp), Schmidt hammer rebound number (SHR), point load strength index (PLI) and thermal conductivity (k) were taken as input variables, whereas UCS and E has been taken as output variables. Several machine learning algorithms were established, and consequently, several approaches were followed for predicting UCS and E of rock samples. The performance of the model reveals that the neural network technique predicts UCS and E with a high rank of accuracy. Moreover, in order to modify the Hoek’s models of rock mass properties distribution based on his experience, a computational standard deviation has been proposed in ths study. The standard deviation of the data obtained from the best neural network architecture has been further used as a base to propose a state-of-the-art model for the probability distribution prediction of UCS and E. Hence, Monte Carlo simulations stipulates that this approach is more reliable for prediction of probability distribution of UCS and E of the various rock samples. This stochastic approach can be considered as a keystone to predict the probabilistic analysis of various geomechanical characterizations of rock samples.