Alice and Bob have three children, and everyone lives in the same household. One day, all three children have an infectious disease. The spread of the infection through the household is to be modeled as a stochastic simple epidemic with infectious contact rate 3 = 2 per day. When there are y infectious, let , denote the epidemic rate. (a) Write down an expression for the epidemic rate 3,, and calculate the values of B3, B, and 8. (b) What is the expected waiting time until one of the two (Alice and Bob) catches the disease? (c) What is the expected waiting time until all five family members have caught the disease? A (d) What is the standard deviation of the waiting time until all five family members have caught the disease? (e) What is the probability mass function of the number of infectives at time t? (f) What is the expected number of infections after one day? [1] [3] [2] [7] [3]