Let fx b For that value of c find P7 X 7 Round your answ

Let

f(x) =

.
(b) For that value of c, find

P(7 < X < 7).

(Round your answer to three decimal places.)

Solution

f(x)=C/(1+X^2)

For f(x) to be a probability density function the integral over the number line must equal 1.

we have:
f(x) dx = 1
c ( arctan() - arctan(-)) = 1
c = 1
c = 1/  

P( -7< X < 7 ) =
7
f(x) dx
-7
= (1.4288 - ( -1.4288))/ = 0.9095