. A student randomly guesses on multiple choice exam (and hence independence between each question can be assumed). There are four questions, each question has five options. Let X be the random variable for the number of correct guesses. Write the distribution for X. Determine the probability of answering exactly 3 questions correctly. Determine the probability of answering at most 2 questions correctly. Determine the expected number of correct guesses (long run average of the correct guesses), and the variance of number of correct guesses.

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