Q-I) 14 marks Two stations communicate by sending packets over a wireless channel. In each time...

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Q-I) 14 marks Two stations communicate by sending packets over a wireless channel. In each time slot, each station indepen- dently attempts to send a packet with a probability of 1. If both stations send a packet simultaneously, the packets collide and are not received. Define Y as the number of time slots required until a successful transmission occurs. (a) (2 marks) Define the sample space S for this experiment and determine the probabilities for each basic outcome. (b) (2 marks) Illustrate how S is related to the possible outcomes of Y. (c) (2 marks) Calculate the probability distribution for the different outcomes of Y. 1 Now, assume that station 1 transmits with a probability of - in any given time slot, while station 2 transmits with a probability p. (d) (2 marks) Determine the probability mass function (pmf) for the number of attempts Y until a packet is successfully sent. (e) (2 marks) Assuming a packet has been successfully transmitted, compute the probability that it was sent by station 2. (f) (2 marks) Find the moment generating function of Y. (g) (2 marks) Use the moment generating function. Find the mean and variance of Y. Q-I) 14 marks Two stations communicate by sending packets over a wireless channel. In each time slot, each station indepen- dently attempts to send a packet with a probability of 1. If both stations send a packet simultaneously, the packets collide and are not received. Define Y as the number of time slots required until a successful transmission occurs. (a) (2 marks) Define the sample space S for this experiment and determine the probabilities for each basic outcome. (b) (2 marks) Illustrate how S is related to the possible outcomes of Y. (c) (2 marks) Calculate the probability distribution for the different outcomes of Y. 1 Now, assume that station 1 transmits with a probability of - in any given time slot, while station 2 transmits with a probability p. (d) (2 marks) Determine the probability mass function (pmf) for the number of attempts Y until a packet is successfully sent. (e) (2 marks) Assuming a packet has been successfully transmitted, compute the probability that it was sent by station 2. (f) (2 marks) Find the moment generating function of Y. (g) (2 marks) Use the moment generating function. Find the mean and variance of Y.