GATE 2017 EE (EE2) – Question 27

Engineering Mathematics · Probability and Statistics: Random variables · 1 mark · Numerical answer

A traffic light repeats 2 minutes of green (no stop) followed by 3 minutes of red (stop). Vehicle arrivals are uniform over the 5-minute cycle. The expected waiting time in minutes is ________.

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Correct answer: 0.9 to 0.9

Explanation

A vehicle arrives during red with probability 3/5. Conditional on a red arrival, its remaining red time is uniform from 0 to 3 minutes, with mean 1.5 minutes.

Green arrivals wait zero. Therefore $E[W]=(3/5)(1.5)+(2/5)(0)=$ **0.9 minutes**. Averaging only over stopped vehicles would instead give 1.5, which is not the requested unconditional mean.

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