I'm struggling with this assignment. If someone would be able to complete it for me, entirely, it would be greatly appreciated.

Pg. 2/4. 3. Buses arrive at a specied stop at 15-minute intervals starting at 7:00 A.M. That is, they arrive at 7:00, 7:15, 7:30, 7:45,..... A passenger arrives at the stop with probability f(x): 1/30 if 0 3x530 f = (X) l 0 otherwise Where X is the R.V. denoting the number of minutes passed 7:00 that the passenger arrives at the stop. As is evident, the passenger only arrives at the stop between 7:00 7:30 A.M. What is the probability that the passenger: A. Waits less than 5 mins. for a bus? B. Waits more than 10 mins. for a bus? 4. Let X denote the RV. that equals the number of tails minus the number of heads when N fair coins are ipped. A. What is the expected value of X? B. Prove that the variance of X equals N. Pg. 3/4. 5. Divide, at random, a horizontal line segment of length ve. Let X: length of the le-hand part. Given: Cumulative Distribution Function of X. 0 ifx S O F(x)= x/S if 0 5. Compute: A. P.D.F. x)? B. E[X]? C. E[S -X]? D. Does E[X(5 X)] = E[X] E[5 X]? 6. Discrete random variables X and Y, whose values are positive integers, have the joint probability mass function: 130% Y) = 2_x_y - A. Determine the marginal probability mass functions p(x) and p(y). B. Are X and Y independent? C. Determine E[X], E[Y], and E[XY]. 7. Suppose that random variables X and Y have a joint density function given by: = x+y if 05x51,0_ 100 What is the probability that exactly 2 out of the 5 subsystems in this complex system, will have to be replaced within the rst 150 hrs. of operation? 2. Compute the Cumulative Distribution Function for the function f(x) in problem 1. A. P(X 3100)? B. P(X 5130)? C. P(X >140)? D. P(110 s X $120)