Let $f ( x ) = 8 x e ^ { - 4 x ^ { 2 } } , x > 0$

Let $f ( x ) = 8 x e ^ { - 4 x ^ { 2 } } , x > 0$ be the probability density function of a random variable X. Find the median of the probability density function $f$ .

A) $\frac { \ln \sqrt { 2 } } { 2 }$
B) $\frac { \ln \sqrt { 3 } } { 2 }$
C) $\frac { 1 } { 2 }$
D) $\frac { 2 } { 3 }$
E) $\frac { \ln 2 } { 2 }$
F) $\frac { \sqrt { \ln 2 } } { 2 }$
G) $\frac { \sqrt { \ln 2 } } { 4 }$
H) $\frac { 1 } { 4 }$

Correct Answer:

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