Classical trust model for Peer to Peer networks calculates the global trust value by iteration of local trust value. Every transaction will cause iteration throughout the whole networks resulting in huge communication traffic and computational complexity. Collusion attack, sleeping attack, slander attack, and so on are also faced, which are caused by sparse transactions data and inaccurate computing results. To ensure the density of transaction data and the accuracy of computing results, the paper presents a novel Peer to Peer trust model based on theory of probability and statistics. The history records of transactions are used to figure out the trust value of every peer with the maximum likelihood estimation and hypothesis testing. Every peer trades with other peers with high credibility. Mathematical analysis and simulation show it can resist attacks of malicious peers and improve the successful download rate of the whole Peer to Peer system compared with classical model Eigentrust.