Question

An optical communication system transmits information at a rate of 109 bits/sec. The probability of a bit error in the optical communication system is 10-9. Find the probability of five or more errors in 1 second.

Answer 1

Answer:-

Given That:-

An optimal communication system transmits information at a rate of 10⁹ bits/sec.

The probability of a bit error in the optical communication system is 10^-9.

It is actually a binomial model with n=10⁹ and p =10^-9...

but it can be approximated as poison model as n is large and p is small and the product np is constant =1

hence it can be approximated as Poisson (1)

hence probability of atleast 5 errors = P(X$\geq$5)
where X follows Poisson (1 )

P(X $\geq$ 5) = 1 - P(X<5)

= 1 - 0.9963

= 0.0037