Lecture Notes Example 3.12.pdf - 3.12 f(x = If x < 1 F(x = If 1 x < 2 F(x = If x Z x • f(t dt = x2 3 0 Z x • Z 1 • if 1 x < 2 elsewhere f(t dt = 0

# Lecture Notes Example 3.12.pdf - 3.12 f(x = If x < 1 F(x =...

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3.12. f ( x ) = ( x 2 3 , if - 1 x < 2 0 , elsewhere . If x < - 1, F ( x ) = Z x - f ( t ) dt = Z x - 0 dt = 0 If - 1 x < 2, F ( x ) = Z x - f ( t ) dt = Z - 1 - 0 dt + Z x - 1 t 2 3 dt = 0 + t 3 9 x - 1 = x 3 + 1 9 If x 2, F ( x ) = Z x - f ( t ) dt = Z 1 - 0 dt + Z 2 - 1 t 2 3 dt + Z x 2 0 dt = 0 + 1 + 0 = 1 So, the CDF of X is F (

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