Detection Theory: Binary Hypothesis Testing: Bayes’ Criteria; Likelihood Ratio Test; Neyman-Pearson Tests; mini-max test; Receiver Operating Characteristics. Parameter Estimation Theory: Random parameter Estimation. Bayes’ Procedure; Minimum Mean Square Error (MMSE) Estimator, Maximum A-Posteriori ( MAP) Estimator. Nonrandom Parameter Estimation; MAP Estimator; Unbiased Estimators and Cramer-Rao (C-R) Bound; Higher Order Bounds. Uniformly Minimum Variance Unbiased Estimators (UMVUE); Sufficient Statistic; Rao-Blackwell Theorem.Multiple Parameter Estimation; Fisher Information Matrix.Composite Hypothesis Testing;Series Representation of Stochastic Processes with Rational spectra; Detection of distinct signals in white noise and colored noise;M-ary Detection and Estimation of signals in white noise and colored noise.