You have two sensors that can be active or asleep in 3 different time slots. Each sensor is independent

and active with probability p=1/2 in each slot, and the slots are independent of one another. Consider the

following:

. Event A; = both sensors are active in slot i. . Events A; and A; are independent if i / j. . Event B = the two sensors are active in all three time slots. . The random variable X = 1 if event B occurs, and X = 0 otherwise. Answer these questions: 1. What is P(X = 1)? 2. To what family of distributions does the distribution of X belong? Provide this answer as X ~ distri- bution_name(parameters). See the lecture notes for examples. 3. What is the value of E(X )? 4. What is the value of Var(X)