Leukemia is a life-threatening disease. So far diagnosing of leukemia is manually carried out by the Hematologists that is time-consuming and error-prone. The crucial problem is leukocytes' nuclei segmentation precisely. This paper presents a novel technique to solve the problem by applying statistical methods of Gaussian mixture model through expectation maximization for the basic and challenging step of leukocytes' nuclei segmentation. The proposed technique is being tested on a set of 365 images and the segmentation results are validated both qualitatively and quantitatively with current state-of-the-art methods on the basis of ground truth data (manually marked images by medical experts). The proposed technique is qualitatively compared with current state-of-the-art methods on the basis of ground truth data through visual inspection on four different grounds. Finally, the proposed technique quantitatively achieved an overall segmentation accuracy, sensitivity and precision of 92.8%, 93.5% and 98.16% respectively while an overall F-measure of 95.75%.