See the Image When network cards are communicating bits can

See the Image

When network cards are communicating, bits can occasionally be corrupted in transmission. Engineers have determined that the number of bits in error follows a Poisson distribution with mean of 3.2 bits/kb. What is the probability of 5 bits being in error during the transmission of 1kb? What is the probability of 8 bits being in error during the transmission of 2kb? What is the probability of no error in 3 kb?

Solution

a)

Note that the probability of x successes out of n trials is          
          
P(x) = u^x e^(-u) / x!          
          
where          
          
u = the mean number of successes =    3.2      
          
x = the number of successes =    5      
          
Thus, the probability is          
          
P (    5   ) =    0.113979383 [answer]

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b)

Here, in 2 kb, there are 3.2 bits/kb (2 kb) = 6.4 bits = mean.

Note that the probability of x successes out of n trials is          
          
P(x) = u^x e^(-u) / x!          
          
where          
          
u = the mean number of successes =    6.4      
          
x = the number of successes =    8      
          
Thus, the probability is          
          
P (    8   ) =    0.115993749 [answer]

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c)

Here, in 3 kb, there are 3.2*3 = 9.6 average errors.

Note that the probability of x successes out of n trials is          
          
P(x) = u^x e^(-u) / x!          
          
where          
          
u = the mean number of successes =    9.6      
          
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.0000677287 [ANSWER]