This course provides a one-semester introduction to the theory of probability and mathematical statistics, suitable as background for more advanced 400-level statistics courses such as 36-401 and 36-402 (Modern Regression and Topics in Data Analysis). The course will emphasize probability models and distribution theory; the practice of statistical inference based on the use of maximum likelihood estimation; and applications of statistical modeling and inference, using case studies drawn from the social, physical and biomedical sciences. The use of a computer software package will be an integral part of this course. Students who have taken 36-225 or 36-326 may not receive credit for this course. Students who have take 73-360 need permission of the instructor. Prerequisites: 21-112 or 21-120 and one of 36-203 or 36-247 or 36-309 or 36-208.