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 hour2 independently of other hoursz the system opetattes at full speed with probability %, it operates at half speed with probability %, 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 rst 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 =