HOMEWORK 3 STAT 414 Fall 2022 I. (30 points) A multiple-choice test consist of 4 questions, each with 3 possible options (only one is correct), and a student is answering the questions independently at random (each option equally likely to be selected) Suppose that X is the random variable that counts the number of correct answers minus the number of mistakes. (a) Write dcwn the sample space Q and the random variable X (i.e., the function for each w Q). (b) Find the probability mass function (pmf) of X _ (c) Find the cumulative distribution function (cdf) of X _