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Consider a Slotted-ALOHA system with N nodes. Each node transmits a packet in a slot with probability 0.3 . Find the following: a. The probability

Consider a Slotted-ALOHA system with N nodes. Each node transmits a packet in a slot with probability 0.3. Find the following:

a. The probability that there is a successful transmission.

b. The probability that a slot is idle.

c. The probability of a collision.

d. The probability that 3 consecutive slots would be idle (i.e., no transmissions).

e. The probability that at least 5 (assuming N > 5) nodes transmit in a slot.

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