ABSTRACT: In this paper, we have considered a size biased Exponential distribution (SBED), a particular case of the weighted exponential distribution, taking the weights as the variate values. Moments of the distribution are derived. Maximum likelihood estimation is also discussed. We also present Bayes’ estimator of the parameter of Size biased exponential distribution (SBGMD), that stems from an extension of Jeffery’s prior (Al-Kutubi (2005)) with a new loss function (Al-Bayyati (2002)). We are proposing four different types of estimators. Under squared error loss function, there are two estimators formed by using Jaffrey prior and an extension of Jaffrey’s prior. The two remaining estimators are derived using the same Jeffrey’s prior and extension of Jeffrey’s prior under a new loss function. We are also deriving the survival functions of the size biased exponential distribution under the Jaffrey’s prior and an extension of the Jaffrey’s prior. These methods are compared by using mean square error through simulation study with varying sample sizes.