Consider the four-question quiz. The following lists all the possible outcomes in the sample space. For example, SSSF means a student answered the first three questions correctly (Success) and the fourth incorrectly (Eailure). (SSSS SSSF SSFS SSFF SESS SESE SFFS SFFF FSSS ESSE FSFS FSFF FFSS FESE FFFS FFFF} How many possible outcomes are there? Explain why this makes sense by way of the Fundamental Counting Principal? Determine the value of the random variable X = "number of correct answers" for each outcome in the sample space. Is X a discrete or a continuous random variable? How many of these 16 outcomes contain exactly one success and three failures? Is the empirical estimate of the probability that X = 1 close to 4/16? Explain why this is not the case. # correct #of students Empirical Probability 0,25 0 5 0.35 17 0.3 26 0.15 3 33 3 0 40 0 Total 20