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If f(x)= x 8 , if 0 < x < 4=0 , otherwise is probability density function (p.d.f) of c.r.v. X and F(x) is c.d.f. associated with f(x) , then F (0 5)=

Options

  1. A1 64
  2. B1 8
  3. C1 32
  4. D1 128

Correct answer

A. 1 64

Step-by-step solution

F(x)= ₀^ x f(y) d y= ₀^ x y 8 d y= 1 8 [ y² 2 ]₀^ x = 1 16 (x²-0 )= x² 16 F(0.5)= (0.5)² 16 = 1 4 16 = 1 64

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