At this moment writing this I just want to remind myself of some pretty interesting problems in probability that I have encountered in the past few days. Without wasting any time let me just begin :
In an independent trials of a fair dice , what is the probability that 1 will show up before 6 ?
There are s urns and n balls (n>s) to be distributed among them. What it the expected value of the variable Y(k) which indicates the number of urns that have exactly k balls ? Its variance ?
What is the expected value of number of flips which is conducted in this manner : I keep on flipping a fair coin until I get two tails ? (Hint: derive it knowing that the expected number of flips that are done before one gets a head is 1)
So there are n nodes that want to send their packets in the next given time slot. Each of them has probability p of transmitting a packet. What is the probability there is a collision ? What is the probability that a packet finds a collision ? (Hint: the two answers are different)
Will update as I find some more !
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