Thread: 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.

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



CB

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).