In a college in Georgia, suppose 30 students enroll in an online spring semester statistics course....

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In a college in Georgia, suppose 30 students enroll in an online spring semester statistics course. Also, 35 students enroll in the same semester into a calculus online class. In general, the students do not tend to take both calculus and statistics at the same time, and the two courses are offered to students in different degree programs. Suppose 15% of students that take statistics fail the first test. Also, 10% of students that take calculus fail the first test. Let X be the number of students that fail the first statistics test; and Y be the number of students that fail the first test. Find the following. (a) Write in words what the random variable Z = X + Y measures or represents in this problem. State the support of Z. (b) Write an expression for the distribution of Z. (c) Find the expected value of Z, given that five students failed the first calculus test. (d) Find the moment generating function of the random variable Z. In a college in Georgia, suppose 30 students enroll in an online spring semester statistics course. Also, 35 students enroll in the same semester into a calculus online class. In general, the students do not tend to take both calculus and statistics at the same time, and the two courses are offered to students in different degree programs. Suppose 15% of students that take statistics fail the first test. Also, 10% of students that take calculus fail the first test. Let X be the number of students that fail the first statistics test; and Y be the number of students that fail the first test. Find the following. (a) Write in words what the random variable Z = X + Y measures or represents in this problem. State the support of Z. (b) Write an expression for the distribution of Z. (c) Find the expected value of Z, given that five students failed the first calculus test. (d) Find the moment generating function of the random variable Z.