| the ice. Let X aqua WES-03: A tetrahedron (four-sided die with outcomes 1 2 3r 4' ls \"Had M sum of the two outcomes. a] What are the possible values for X P b} Display the density function forx as a table. c} Check that Ex) =1- ailx pr>61=? \f\"1 \"Newman-hum ti nd the variance and standard deviation am d} Find the moment-generating function ant 1,933.05: The following discrete distribution X represents the number of students seen in a statistics professofs office over the course of any given day. 1] 1 2 3 4 0.31 0.45 0.15 0.05 0.03 val ls x} a valid density function? Why or why:I not? b) E[X] = ?? c) Var[X] = ? d) f(3) = ? e) F(2) = ?? f) What is the probability the statistics professor will see at least 2 students on any given day? g) What is the moment-generating function for X?\ftickets. f) Using F[X], find the probability that at least five attempts must be made in order to purchase g) Find the expected value, E[X]. h) Find the moment-generating function for X. WB3-07: A student takes a 3-question quiz. Each question has 5 possible answers (1 correct). He guesses at random. Let X = the number he gets correct. (a) Display the density function for X as a table. Check that Ef ( x) =1 all x (b) Write a formula for f.\fWB3-09: Suppose X and Y are two independent random variables with E[X] = 6, E[Y] = 2, E[X] ] = 52, and E[Y2] = 10. a) Find E[5x + 3y -2] 20 b) Find Var[3X - 4Y + 6] c) Find Var *-5]