When we randomly select an element, needed for our study, from a population of interest and mix it again with the same population so that it may be selected again. We say that we did sampling with replacement. In sampling with replacement the same element may be selected more than once from the population of interest. In this method of sampling all the possible events are independent of each other and their covariance is zero. In other words the occurrence of one event has no effect upon the occurrence of other event. And the probabilities of their occurrence remains equal regardless the frequency of each event in the process. For example in throwing a dice, each number (1-6) on the dice has 1/6 probability of being selected, no matter how many times we throw it. For sampling without replacement click here.
