The missing data problem has been broadly studied in the last few decades and has various applications in different areas such as statistics or bioinformatics. Even though many methods have been developed to tackle this challenge, most of those are imputation techniques that require multiple iterations through the data before yielding convergence. In addition, such approaches may introduce extra biases and noises to the estimated parameters. In this work, we propose novel algorithms to find the maximum likelihood estimates (MLEs) for a one-class/multiple-class randomly missing data set under some mild assumptions. As the computation is direct without any imputation, our algorithms do not require multiple iterations through the data, thus promising to be less time-consuming than other methods while maintaining superior estimation performance. We validate these claims by empirical results on various data sets of different sizes and release all codes in a GitHub repository to contribute to the research community related to this problem.