Question

Suppose that the mobile company central computer handles 60 million text messages a second. For each text message it handles assume that there is an (independent) one in twelve million chance that it will be missed.

What is the expected number of missed test messages in a second?

What is the variance of the number of missed test messages in a second?

What are the chances that the central computer misses exactly four test messages in the next second? (Use an Poisson approximation)

Answer 1

a) The expected number of missed text messages in a second is computed here as:

= np

Where n is the total number of messages handled in a second * Probability of missing a message

= 60/12

= 5

Therefore 5 is the expected number of missed test messages in a second here.

b) The variance of the number of messages missed is computed here as:

= np(1-p)

Note that as p is so small, 1 - p is approx. 1

c) As mean = Variance here, therefore the distribution of the number of missed messages here could be modelled as:

The probability that the central computer misses exactly four test messages in the next second:

Therefore 0.1755 is the required probability here.