Statistical inference problems in communications and signal processing are studied in this course. Problems are classified into those with vector observations, sequence observations, and continuous-time waveform observations. They are also classified into detection and estimation problems, and into those with random parameters and non-random parameter. Optimality criteria discussed in this course include MAP, ML, MMSE, MVUE, and LS. For each optimality criterion, an optimal solution is derived and their performance is analyzed.