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MHT CET202314 May 2023Morning ShiftMathematicsProbabilityActual

If f (x)= cases 3 (1-2 x^2 ) & ; 0 < x < 1 0 & ; otherwise cases is a probability density function of X , then P ( 1 4 < x < 1 3 ) is

Options

  1. A75 243
  2. B23 96
  3. C179 864
  4. D52 243

Correct answer

C. 179 864

Step-by-step solution

aligned P ( 1 4 < x < 1 3 )= & _ 1 4 ^ 1 3 f (x) d x= _ 1 4 ^ 1 3 3 (1-2 x^2 ) d x & = [3 x-2 x^3 ]_ 1 4 ^ 1 3 & = (1- 2 27 )- ( 3 4 - 1 32 ) & = 1 4 + 1 32 - 2 27 & = 179 864 aligned

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