5.97 National security requires that defense technol- ogy be able to detect incoming projectiles or missiles. To make the defense system successful, multiple radar screens are required. Suppose that three independent screens are to be operated and the probability that any 1 one screen will detect an incoming missile is 0.8. Ob- viously, if no screens detect an incoming projectile, the 5.6 Potential Misconceptions and Hazards number of heads. The students in each group should individually compute the proportion of heads observed, which is an estimate of p, the probability of observing a head. Thus, there will be a set of values of p (from group 1) and a set of values p2 (from group 2). All of the values of pi and p2 are estimates of 0.5, which is the true value of the probability of observing a head for a fair coin. (a) Which set of values is consistently closer to 0.5, the values of pi or p2? Consider the proof of Theorem 5.1 on page 147 with regard to the estimates of the parameter p=0.5. The values of p were obtained with n = n = 10, and the values of p2 were ob- tained with n = n2 = 40. Using the notation of the proof, the estimates are given by P = = 721 where I1,..., In, are Os and Is and n = 10, and 22 P2= = 112 112 where I1,..., In2, again, are Os and is and n = 40