consider time slot data transmission from a base station to a node. In each time slot, the base station transmits a packet with probability 0.4. The node can be in the active mode and can receive the packet, the power consumption of which is 30 mW. Alternatively, the node can be in the sleep mode and cannot receive the packet, the power consumption of which is 10 mW. The node can decide to be in the receive mode or sleep mode with probability p. Calculate an optimal value of probability p such that the average power consumption of the node is minimized, and the base station achieves the throughput of 0.3 packets/time slot. Compute the average power consumption at the optimal value of probability p.