3.3 A wireless packet communications channel su ers from clustered errors. That

Question

3.3 A wireless packet communications
channel su ers from clustered errors.
That is, whenever a packet has an error,
the next packet will have an error with
probability 0:9. Whenever a packet is
error-free, the next packet is error-free
with probability 0:99. In steady-state,
what is the probability that a packet has
an error?

k such that P q for every state i. Prove that the probability of state k at any time n 1 is pk (n) q. Sket 3.3 A wireless packet communications stat channel suffers from clustered errors. 5.4 That is, whenever a packet has an error, the next packet will have an error with proba probability 0.9. Whenever a packet is With error-free, the next packet is error-free "club with probability 0.99. In steady-state you re what is the probability that a packet has visit f an error receive 4.1 For the Markov denote chain in Proh onud

Explanation / Answer

P(current packet has a error) = P(current packet has an error, given that preceding packet also has an error) +

P(current packet has an error, given that preceding packet has NO error)

From the data given we have:

P(current packet has an error, given that preceding packet also has an error) = 0.90

P(current packet has an error, given that preceding packet has NO error) = 1-0.99 = 0.01

So, required probability is:

P(current packet has a error) = 0.90 + 0.01 = 0.91

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