Hi everyone, I am stuck on this question:
A multiple choice exam, each with 5 possible answers. One mark is awarded for a correct answer, and 1/4 mark is deducted for an incorrect answer. A particular student has probability p(i) it knowing the answer to the i-th question, independently of other questions.
Suppose that on a question where the student does not know the answer, he or she guesses randomly. Show that his or her total mark has expectation