2. There was a robbery in Springeld and the suspect is on trial. Luckily, there was an eyewitness who has identied the defendant as guilty. Unluckily, she's pretty mistrustful of \"all the indistinguishable young rascals\" in her neighborhood. Your guess is that she would correctly report a guilty person's guilt 95% of the time. However, you also think she'd incorrectly report an innocent person's guilt 75% of the time. (By the way, the Innocence Project they use DNA to exonerate the falsely imprisonedhas shown that 76% of all felony convictions that are eventually overturned were originally based on eyewitness testimony.) You remember hearing somewhere that about two thirds of felony defendants are actually guilty {that they actually committed the crimes for which they are tried} so you are anchored on that as a prior probability of the defendant's guilt. a. What is your prior probability that a random defendant is guilty? HG) = b. What is your prior probability that a random defendant is not guilty? P(~G) = c. What is your conditional probability that the eyewitness would say the defendant is guilty given that he is? PthJG) = d. What is your conditional probability that the eyewitness would say the defendant is guilty given that he isn't? masts) = e. What is the eyewitness's false negative rate? That is what is the chance she fails to identify a guilty person? {You gure out what conditional probability I'm asking for.) f. Use the answers from a-d to determine your conditional probability that the defendant is guilty given the eyewitness says he is. PlfGr'E} =