(a) Show that $p ( x ) = \left\{ \begin{array} { l l }
( 2 - k ) x ^ { - 3 + k } & \text { if } x \geq 1 \
0 & \text { otherwise }
\end{array} \right.$ where k is fixed and $0

Question

(a) Show that $p ( x ) = \left\{ \begin{array} { l l } 
( 2 - k ) x ^ { - 3 + k } & \text { if } x \geq 1 \
0 & \text { otherwise }
\end{array} \right.$ where k is fixed and $0 < k < 1$ is a probability density function.(b) What is the mean for this distribution?
(c) Calculate the median of $p$

Quizplus · Accepted Answer

The Answer of (a) Show that $p ( x ) = \left\{ \begin{array} { l l } 
( 2 - k ) x ^ { - 3 + k } & \text { if } x \geq 1 \
0 & \text { otherwise }
\end{array} \right.$ where k is fixed and $0 < k < 1$ is a probability density function.(b) What is the mean for this distribution?
(c) Calculate the median of $p$

(A) Show That p(x)={(2−k)x−3+k if x≥10 otherwise p ( x ) = \left\{ \begin{array} { l l } ( 2 - k ) x ^ { - 3 + k } & \text { if } x \geq 1 \\0 & \text { otherwise }\end{array} \right.p(x)={(2−k)x−3+k0​ if x≥1 otherwise ​

(A) Show That $p ( x ) = \left\{ \begin{array} { l l } ( 2 - k ) x ^ { - 3 + k } & \text { if } x \geq 1 \\0 & \text { otherwise }\end{array} \right.$