# uniform distribution problem

• Mar 27th 2011, 08:25 PM
Evan.Kimia
uniform distribution problem
Let X have the uniform distribution U(0,1). Find the distribution function and then the p.d.f of Y = -2lnX

hint: Find P(Y<=y) = P(X>=e^(-y/2) when 0 <y < infinity)

Im having a hard time solving this problem, could anyone help me start it/give suggestions? Thanks.
• Mar 27th 2011, 08:40 PM
CaptainBlack
Quote:

Originally Posted by Evan.Kimia
Let X have the uniform distribution U(0,1). Find the distribution function and then the p.d.f of Y = -2lnX

hint: Find P(Y<=y) = P(X>=e^(-y/2) when 0 <y < infinity)

Im having a hard time solving this problem, could anyone help me start it/give suggestions? Thanks.

$P(Y\le y)=P(-2\ln (X)\le y)=P(X\ge e^{-y/2})= ...$

and

$f_Y(y)=\dfrac{\partial}{\partial y} P(Y\le y)$

CB
• Mar 28th 2011, 01:05 AM
mr fantastic
Quote:

Originally Posted by Evan.Kimia
Let X have the uniform distribution U(0,1). Find the distribution function and then the p.d.f of Y = -2lnX

hint: Find P(Y<=y) = P(X>=e^(-y/2) when 0 <y < infinity)

Im having a hard time solving this problem, could anyone help me start it/give suggestions? Thanks.

And when you think you have the answer, you can use the Probability Integral Transform Theorem to check it - the calculation takes 2 lines - (and if you're allowed to ignore the hint, you can go straight to the theorem).