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GATE 2019 CE (CE2) – Question 36

Engineering Mathematics · Probability and Statistics: Random variables, Poisson and Normal distributions, linear regression · 2 marks · Multiple choice

A continuous random variable is uniformly distributed between x and y, with y > x. Find its probability density inside this interval.

  1. $1/(x-y)$
  2. $1/(y-x)$
  3. $x-y$
  4. $y-x$

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Show answer and explanation

Correct answer: (B) $1/(y-x)$

Explanation

Uniform probability density f satisfies $f(y-x)=1$ when integrated over its support. Thus **f = 1/(y − x), B** inside the interval, and zero outside.