Let $$f ( x ) = \left\{ \begin{array} { l l }
\frac { k \ln x } { x ^ { 4 } } & \text { if } x 1 \
0 & \text { otherwise }
\end{array} \right.$$ (a) Find k so that f can serve as the probability density function of a random variable X.(b) Find $P ( X e )$ .(c) Find the mean.

Question

Let $$f ( x ) = \left\{ \begin{array} { l l } 
\frac { k \ln x } { x ^ { 4 } } & \text { if } x > 1 \
0 & \text { otherwise }
\end{array} \right.$$ (a) Find k so that f can serve as the probability density function of a random variable X.(b) Find $P ( X > e )$ .(c) Find the mean.

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The Answer of Let $$f ( x ) = \left\{ \begin{array} { l l } 
\frac { k \ln x } { x ^ { 4 } } & \text { if } x > 1 \
0 & \text { otherwise }
\end{array} \right.$$ (a) Find k so that f can serve as the probability density function of a random variable X.(b) Find $P ( X > e )$ .(c) Find the mean.

Let f(x)={kln⁡xx4 if x>10 otherwise f ( x ) = \left\{ \begin{array} { l l } \frac { k \ln x } { x ^ { 4 } } & \text { if } x > 1 \\0 & \text { otherwise }\end{array} \right.f(x)={x4klnx​0​ if x>1 otherwise ​

Let $f ( x ) = \left\{ \begin{array} { l l } \frac { k \ln x } { x ^ { 4 } } & \text { if } x > 1 \\0 & \text { otherwise }\end{array} \right.$