I'm aware of the conditions of a CDF. to be a cumulative distribution: it is always nonnegative, when x→−∞ x→−∞ it tends to 0, when x→+∞ it tends to 1, and it is right-continuous .

  • 1
    $\begingroup$ Note: this is the CDF of the uniform distribution over [0,1], classically denoted by U (0,1). $\endgroup$ – Harry49 Mar 16 '17 at 8:44
  • $\begingroup$ $F(x)=\min(1,\max(0,x))$ works but is not as simple to read or understand as the definition in three pieces $\endgroup$ – Henry Mar 16 '17 at 9:03

The CDF is proportional to $x$ if it has the form $F(x)=cx$, for some constant $c$. You need that, for $x<0$, $F(x)=0$, and for $x>1$, $F(x)=1$.

What constant $c$ makes it such that $F(0)=0$, $F(1)=1$?

$F(0)=c\cdot0=0$ always.

$F(1)=c\cdot1=1$, so we need $c$ to be equal to 1.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.