Here statistical technique of assigning probabilities to randomly evolved sample paths in coin-toss space is discussed. The intuition carries into continuous time stochastic processes as well. Conditional expectation, one of the key concepts, is discussed and results are produced to make the conceptions clear on how this estimates work. All these results are valid in continuous time math finance area and act as primary tools in this research arena. Martingale, another useful notion, is defined and all related Martingales in binomial asset pricing model are reported as they develop mathematically. The program on conditional expectation given in Chapter III basically helps us to build another useful code on Martingale. A program, given in Chapter-IV and with this Elaborations and discussions are produced to convince what really carrying information through Sigma-algebra in Binomial model means. Chapter-V finally deals with the fact why studying Binomial model is important. A detailed study shows the convergence of Binomial option prices to the celebrated Black-Scholes option prices, where the importance lies.