The discussion focuses on deriving the probability density function (p.d.f) of a random variable Y defined as Y = 1/X, given the p.d.f of X. The p.d.f of X is defined piecewise: fx(X) = 1/4 for 0 < x < 1 and fx(X) = 3/8 for 3 < x < 5. To find fy(y), the relationship between P(X < x) and P(X > x) for continuous distributions is crucial. The solution involves computing G(t) = P(X > t) based on the provided p.d.f of X.
PREREQUISITESStudents in statistics or probability courses, mathematicians, and anyone interested in understanding transformations of random variables and their applications in probability theory.
wldnrp13579 said:Homework Statement
fx(X) ={ 1/4 0 < x < 1,
{ 3/8 3 < x < 5,
{ 0 otherwise
Let Y = 1/X. Find the probability density function fy (y) for Y .
Homework Equations
The Attempt at a Solution
Fy(x)=P(Y<x)=P(1/X<x)=P(X>1/x)..
i can't go over more than this