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) $\frac { 1 } { 4 }$

Question

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) $\frac { 1 } { 4 }$

Quizplus · Accepted Answer

The Answer of 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) $\frac { 1 } { 4 }$

Let f(x)=8xe−4x2,x>0f ( x ) = 8 x e ^ { - 4 x ^ { 2 } } , x > 0f(x)=8xe−4x2,x>0

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