Consider a wireless network consists of one access point and N client devices. Slotted ALOHA is adopted in this network. It is assumed that in each slot, a client device sends a packet to the access point with probability. Also, the access point sends a packet to one of the clients with probability pa in each slot. Single packet transmission time is equal to the slot length. Packet transmission by a device is considered to be successful if only one transmission takes place in the slot. (a) Calculate the probability that there is a successful transmission. (b) Calculate the probability that a given transmission by a client device is success- ful. (c) Calculate the probability that a given transmission by the access point is suc- cessful. (d) Let N, and N, denote the average number of packets successfully sent and received by the access point per slot, respectively. As N approaches infinity, find the value of pa such that Ng = Nr.