Packet switched networks are the backbone of the Internet. Here, data is transferred from a source to a destination by encapsulating and transferring data as a series of packets. There are a number of reasons due to which packets get lost in the network and never reach the destination. Consider two models for packet losses in the network.Model $1$: Each packet is lost with probability $?$ independently.Model $2$: A packet is lost with probability $?1$ if its previous packet was transmitted successfully, and is lost with probability $?2$ if its previous packet was lost.Suppose a source sends exactly three packets over the network to a destina$-$ tion. For this setup, under Model $2,$ assume that the probability of the first packet getting lost is $?1.$ Further assume $?=?1=0\mathrm{.}01$ and $?2=0\mathrm{.}5.($a$)$ What is the probability that the second packet is lost under Model $1$and Model $2?($b$)$ Suppose you are told that the third packet is lost. Given this additionalinformation, what is the probability that the second packet is lost underModel $1$ and Model $2?($c$)$ Suppose we represent the loss pattern for the three packets using $0$sand $1$s$,$ where $0$ represents the packet being lost and $1$ represents thepacket being transferred successfully. For example, loss pattern $110$corresponds to the scenario when the first two packets are transferredsuccessfully and the third packet is lost. What is the probability of losspatterns $\{010,100,001\}$ under Model $1$ and Model $2?($d$)$ What do you observe from your answer to the above question? Specif$-$ically, what kind of loss patterns have higher probability in Model $2$ ascompared to Model $1?$Aside: Extensive measurements over the Internet have shown that packet losses in real$-$world networks are correlated. Models similar to Model $2$ are used to model such correlated packet$-$loss scenarios. For example, one such model is called the GilbertElliot model $[23,32].$