Problem: A person is take a multiple choice exam that has 6 questions. Each question has 5 possible choices. The person decides to randomly guess at each problem. Let x be the number of questions the person will answer correctly. Construct the probability distribution, and answer the following:
Find the expected value of x
Find the variance of x
What i know: I know the probability of answering a question correctly is (1/5) and the probability for answering a question incorrectly is (4/5). I also know that each question is independent of the others. To find the probabilities for my distribution I used [(1/5)^n]*[(4/5)^m] where n is the number of correctly answered questions and m is the number of incorrectly answered questions. My probability distribution is:
This doesn't seem like it could be correct. Any help would be appreciated.