Problem 4 [16 points]: There are 135 students in STAT1012 this semester. Suppose the probability that a student live in the Lamma Island is 0.02. Let X be the total number of students from STAT1012 who lives in the Lamma Island. (a) [2 points] What probability distribution (including its parameters) does X follow? (b) [3 points] What is the probability that at most 3 STAT1012 students live in the Lamma Island? (c) [3 points] Sketch the cumulative distribution function (cdf) of X up to x = 3.5. (d) [3 Points] What's the expectation values and variance of X? What's the shape of the distribution of X (Right-skewed, left-skewed or symmetric) (e) [5 points] If we randomly choose 10 students in the class, and find that 5 of them are live in Lamma Island. What conclusion can we draw from it