Multiple choice

A uniformly distributed random variable X with probability density function fx (x) = $\dfrac{1}{10}$(u (x + 5) - u (x - 5)) Where u (.) is the unit step function is passed through a transformation given in the figure below. The probability density function of the transformed random variable Y would be

  1. fy =$\dfrac{1}{5}$(u (y + 2.5) - u (y - 2.5))
  2. fy = 0.5$\delta$ (y) + 0.5$\delta$ (y -1)
  3. fy = 0.25$\delta$ (y + 2.5) + 0.25$\delta$ (y -2.5) + 0.5$\delta$(y)
  4. fy = 0.25$\delta$ (y + 2.5) + 0.25$\delta$ (y -2.5) + $\dfrac{1}{10}$(u (y + 2.5) - u (y - 2.5))
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B Correct answer
Explanation

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