Let $f ( x ) = \frac { 4 c } { \left( 1 + x ^ { 2 } \right) }$.
a) For what value of $c$ is $f$ a probability density function?
b) For that value of $c$, find $P ( - 1

Name: Let $f ( x ) = \frac { 4 c } { \left( 1 + x ^ { 2 } \right) }$. a) For what value of $c$ is $f$ a probability density function? b) For that value of $c$, find $P ( - 1 < X < 1 )$.
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Question

Let $f ( x ) = \frac { 4 c } { \left( 1 + x ^ { 2 } \right) }$.
a) For what value of $c$ is $f$ a probability density function?
b) For that value of $c$, find $P ( - 1 < X < 1 )$.

Quizplus · Accepted Answer

The Answer is

ext { a) } \frac { 1 } { 4 \pi } , ext { b) } \frac { 1 } { 2 }

Let f(x)=4c(1+x2)f ( x ) = \frac { 4 c } { \left( 1 + x ^ { 2 } \right) }f(x)=(1+x2)4c​

Let $f ( x ) = \frac { 4 c } { \left( 1 + x ^ { 2 } \right) }$