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, independently of other hours, the system operates at full speed with probability ?, it operates at half speed with probability s, or it breaks down 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 first breakdown occurs. (a) 2 pt - Find the conditional PMF of F given 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 first 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