This thesis work describes how to apply the stochastic analysis framework, presented in [1] for general priority-driven periodic real-time systems. The proposed framework is applicable to compute the response time distribution, the worst-case response time, and the deadline miss probability of the task under analysis in the fixed-priority driven scheduling system. To be specific, we modeled the task execution time by using the beta distribution. Moreover, we have evaluated the existing stochastic framework on a wide range of periodic systems with the help of defined evaluation parameters. In addition we have refined the notations used in system model and also developed new mathematics in order to facilitate the understanding with the concept. We have also introduced new concepts to obtain and validate the exact probabilistic task response time distribution.    Another contribution of this thesis is that we have extended the existing system model in order to deal with stochastic release time of a job. Moreover, a new algorithm is developed and validated using our extended framework where the stochastic dependencies exist due to stochastic release time patterns. / This is Second Version of the report. Submitted after few modifications made on the order of Thomas Nolte (Thesis Examiner). / START - Stochastic Real-Time Analysis of Embedded Software Systems