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MHT CET202313 May 2023Evening ShiftMathematicsContinuity and DifferentiabilityActual

The c.d.f. F (x) associated with p.d.f. f (x) is

Options

  1. A(A) F (x)=4 x^3+3 x^4
  2. BF (x)=4 x^3-3 x^4
  3. CF (x)=-4 x^3-3 x^4
  4. DF (x)=-4 x^3+3 x^4

Correct answer

B. F (x)=4 x^3-3 x^4

Step-by-step solution

aligned F (x) & = ₀^x 12 x^2(1-x) d x & =12 ₀^x (x^2-x^3 ) d x & =12 [ x^3 3 - x^4 4 ]₀^x & =12 [ x^3 3 - x^4 4 ] & =4 x^3-3 x^4 aligned

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