Another problem for homework 5: Consider a packet of size 10 bits that consists of an 8-bit message and two checksum bits at the end. Bits in the message with an odd index generate one of the checksum bits, and bits in the payload with an even index generate the other, both by XOR sum. A given bit is flipped in transit with probability p and all such bit error events are mutually independent. (a) Find the two-bit checksum if the first 8 bits are, in order, 01101011. (b) Carefully describe the types of bit errors that can be detected by the two-bit XOR checksum. (c) Find a simple expression for the probability that at least one bit error occurs in the received packet. (d) Find the probability that exactly kn errors occur among the even indexed bits or exactly ko errors occur among the others, where ke,ko{0,1,2,3,4,5}. (e) Find the probability that transit bit errors in the packet are detected, given that the messsage has bit errors