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GATE 2021 EE – Question 8

General Aptitude · Quantitative Aptitude: Probability and Combinatorics · 2 marks · Multiple choice

Let $X$ be a continuous random variable denoting the temperature measured. The range of temperature is $[0,100]$ degree Celsius and let the probability density function of $X$ be $f(x)=0.01$ for $0\le X\le100$.

The mean of $X$ is ________.

  1. 2.5
  2. 5.0
  3. 25.0
  4. 50.0

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Correct answer: (D) 50.0

Explanation

For a uniform density on $[0,100]$, the mean is $\int_0^{100}x(0.01)\,dx=0.01\times\frac{100^2}{2}=50$.