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GATE 2017 ME (ME1) – Question 15

Engineering Mathematics · Complex Variables: Analytic functions, Cauchy-Riemann equations, integral theorem, Taylor and Laurent series · 1 mark · Numerical answer

A fair six-faced die is rolled a large number of times. Find the mean of the outcomes.

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Correct answer: 3.5 to 3.5

Explanation

Each face from 1 through 6 has probability $1/6$. The expectation is $E[X]=(1+2+3+4+5+6)/6=21/6=3.5$. By the law of large numbers, the sample mean approaches this expectation as the number of independent rolls grows.

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