3 Conditional probability Consider a device that samples packets on a link. (a)
ID: 3004635 • Letter: 3
Question
3 Conditional probability
Consider a device that samples packets on a link. (a) Suppose that measurements show that 20% of packets are
UDP, and that 10% of all packets are UDP packets with a packet size of 100 bytes.What is the conditional probability
that a UDP packet has size 100 bytes? (b) Suppose 50% of packets were UDP, and 50% of UDP packets were
100 bytes long. What fraction of all packets are 100 byte UDP packets?
6 Cumulative distribution function
(a) Suppose discrete random variable D take values {1, 2, 3,...,i,...} with probability 1/2i. What is its CDF?
(b) Suppose continuous random variable C is uniform in the range [x1, x2]. What is its CDF?
7 Expectations
Compute the expectations of the D and C in Exercise 6.
14 Bernoulli distribution
A hotel has 20 guest rooms. Assuming outgoing calls are independent and that a guest room makes 10 minutes
worth of outgoing calls during the busiest hour of the day, what is the probability that 5 calls are simultaneously
active during the busiest hour? What is the probability of 15 simultaneous calls?
15 Geometric distribution
Consider a link that has a packet loss rate of 10%. Suppose that every packet transmission has to be acknowledged.
Compute the expected number of data transmissions for a successful packet+ack transfer.
16 Poisson distribution
Consider a binomially distributed random variable X with parameters n=10, p=0.1. (a) Compute the value of
P(X=8) using both the binomial distribution and the Poisson approximation. (b) Repeat for n=100, p=0.1
Exponential distribution
Suppose that customers arrive to a bank with an exponentially distributed inter-arrival time with mean 5 minutes. A
customer walks into the bank at 3pm. What is the probability that the next customer arrives no sooner than 3:15?
19 Exponential distribution
It is late August and you are watching the Perseid meteor shower. You are told that the time between meteors is
exponentially distributed with a mean of 200 seconds. At 10:05 pm, you see a meteor, after which you head to the
kitchen for a bowl of icecream, returning outside at 10:08pm. How long do you expect to wait to see the next
meteor?
Explanation / Answer
Ans(3a):
Given that 20% of packets are UDP that means P(UDP) = 0.2
10% of all packets are UDP packets with a packet size of 100 bytes
means P(UDP AND 100) = 0.1
Hence P(100 | UDP) = 0.1/0.2 = 0.5.
Ans(3b):
Similarly P(UDP) = 0.5 and P(100|UDP) = 0.
Hence P(100 AND UDP) = 0.5*0.5 = 0.25
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