The expected number of calls

Question

The expected number of calls in progress in a given cell is 75. Give an upper bound on
P[ X > 85]

Answer 1

Use Markov's inequality: If X is any nonnegative random variable and a > 0,

P(X≥a) ≤ E(x)/a.

 

Therefore,

P (X>85) = P(X≥86) ≤ 75/86 ≈ 0.872.