Finding PDF of uniform distribution

  • #1

Homework Statement



Let X be a uniform random variable in the interval [0,1] i.e., X = U [(0,1)]. Then a new random variable Y is given by Y= g(X), where g(x)= -a. ln(x). Show that Y is exponentially distributed. What is the mean of Y?



Homework Equations



fX(x) = 1/ lambda . exp (-x/ lambda)

0 otherwise


The Attempt at a Solution



Y = g(X) can be computed via FY(y)= Summation 1/ differentiation of g(x) multiplied with Fx(x)
I can't show how this is exponential.

Please help!
 

Answers and Replies

  • #2
lanedance
Homework Helper
3,304
2
so as its constant doesn't [itex]f_X(x)=1[/itex] in [0,1], zero otherwise

then use the fact that the probabilty for a given interval dx and corresponding interval dy must be the same
[tex] |f_X(x)dx| = |f_Y(y)dy| [/tex]
 
  • #3
lanedance
Homework Helper
3,304
2
is that what you tried to do? can you show your working?
 

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