The GATE Grind

GATE 2014 EC (EC4) – Question 32

Communications · Random Processes · 1 mark · Multiple choice

Calls arrive at a telephone exchange with each arrival time independent of earlier and future arrivals. What distribution models the total number of calls in a fixed time interval?

  1. Poisson
  2. Gaussian
  3. Exponential
  4. Gamma

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Show answer and explanation

Correct answer: (A) Poisson

Explanation

Under the intended stationary independent-arrival model with constant mean rate, counts in an interval follow a **Poisson distribution,A**. The exponential distribution describes waiting times between calls, not the integer-valued count. Independence is part of the model; a constant-rate assumption is also implicit.