Conditional Expectation and Martingales

This is a set of very hurriedly compiled notes. It has not been proof-checked and is likely to have some errors. These, though, should be minor errors and maybe cleared up by referring to the relevant texts. The texts that have been used in the preparation of the notes are Feller; Grimmett and Stirzaker; Goswami and Rao; David Williams; and Mitzenmacher and Upfal. The purpose behind the notes is to provide an idea of conditional expectations and martingales while keeping within the ambit of discrete probability. In the future, these notes may be expanded into a more refined set of notes which will also include the more general definitions of conditional expectations and martingales. These notes have been prepared to supplement two one-and-half hour lectures on discrete probability that had been delivered at a workshop on combinatorics at the Applied Statistics Unit of the Indian Statistical Institute on 17 and 18 February, 2011.