7. (Sec. 3.6) Consider sending packets of data through the internet, and we have a counter that determinesthe number of missing/corrupted packets. Suppose that number X has a Poisson distribution withparameter 23.=(a) What is the probability that the counter determines that the transmission has exactly one miss-ing/corrupted packet of data?(b) What is the probability that the counter determines that the transmission has at least 3 missing/corrupted packets of data?(c) If two transmissions of data across the internet arthat at least one of them does not contain a missing/corrupted packet?e independently selected, what is the probability

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Asked Sep 25, 2019
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7. (Sec. 3.6) Consider sending packets of data through the internet, and we have a counter that determines
the number of missing/corrupted packets. Suppose that number X has a Poisson distribution with
parameter 23.
=
(a) What is the probability that the counter determines that the transmission has exactly one miss-
ing/corrupted packet of data?
(b) What is the probability that the counter determines that the transmission has at least 3 miss
ing/corrupted packets of data?
(c) If two transmissions of data across the internet ar
that at least one of them does not contain a missing/corrupted packet?
e independently selected, what is the probability
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7. (Sec. 3.6) Consider sending packets of data through the internet, and we have a counter that determines the number of missing/corrupted packets. Suppose that number X has a Poisson distribution with parameter 23. = (a) What is the probability that the counter determines that the transmission has exactly one miss- ing/corrupted packet of data? (b) What is the probability that the counter determines that the transmission has at least 3 miss ing/corrupted packets of data? (c) If two transmissions of data across the internet ar that at least one of them does not contain a missing/corrupted packet? e independently selected, what is the probability

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Expert Answer

Step 1

As per the question, X follows poisson distribution with mean 0.23

Probability density function of poisson distribution is given by

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e их их Р(X %3D х) - х!

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Step 2

a) Probability that the transmission has exactly one missing/corrupted packet of data is given by

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-0.23 x 0.231 Р(x — 1) - e = 0.1827 1!

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Step 3

b) Probability that the transmission has atleast 3 ...

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P(X < 3) 1 - (P(X = 0) P(X 1) P(X 2)) P(X 3) 1 _ -0.23 x 0.232 -0.23 x 0.23 e-0.23 x 0.231 е е 11 0! 1! 2! 1 - (0.7945 0.1827 0.0210) = 0.001708

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