5. 10 pt _ An Aggie ECE student assembles a high-powered computer system and decides to rent the system out on an hourly basis. At any given hour, ldpendentiy of other hours, the system operates at full speed with probability %, it Operates at half speed with probability %, or it breaks doom with probability %. The student gets $1, $0.5, or $0 for every hour that the system operates at full speed, half speed, or it breaks down, respectively. Let F and H be respectively the number of hours that the system operates at full speed and half speed until the rst breakdown occurs. (a) 2 pt Find the conditional PMF of F giveu H = 1. {b} 3 pt Compute the conditional mean and variance of F given H = 1. Let R be the total amount of rental {in dollars} that the student gets until the rst breakdown. {c} 2 pt. Find the conditional PMF of F given R = 1. {d} 3 pt. Compute the conditional mean and variance of F given R = 1