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MHT CET202013 Oct 2020Evening ShiftMathematicsProbabilityActual

If the probability density function of a continuous random variable is f(x)= x³ 3 if -1 < x < 2=0 , otherwise, then the cumulative distribution function of X is

Options

  1. A1 14 [x⁴-1 ]
  2. B1 10 [x⁴-1 ]
  3. C1 16 [x⁴-1 ]
  4. D1 12 [x⁴-1 ]

Correct answer

D. 1 12 [x⁴-1 ]

Step-by-step solution

c.d.f. of x is given by aligned f ( x ) &= _ -1 ^ x f ( y ) dy = _ -1 ^ x y ³ 3 dy &= [ y ⁴ 12 ]_ -1 ^ x = 1 12 ( x ⁴-1 ) aligned

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