# Distribution function when the range is a singleton [closed]

Let $X$ be a real-valued variable defined on a complete probability space $\left(\Omega,F,P\right)$ with singleton set range $R(X)=\{x\}$ for some $x\in R$.

I would like to be able to do the following:

i) find a distribution function $F_{X}$ of $X$.
ii) find a probability density function $f_{X}$ of $X$ (if it exists)
iii) Draw sketches of $F_{X}$ and $f_{X}$ with some justifications
iv) draw some conclusions from i),ii) and iii) if possible.

I'm a little bit confused as to where to begin. Hints and suggestions would be very much appreciated. Thanks.

-

## closed as off-topic by Did, Normal Human, yoknapatawpha, Ken, Jonas MeyerJul 24 at 2:43

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Did, yoknapatawpha, Ken
If this question can be reworded to fit the rules in the help center, please edit the question.

i) $F_X(t)=0$ if $t<x$ and $F_X(t)=1$ if $t\ge x$. ii) $f_X$ does not exist. iii) Please do. iv) What?
Thanks. I'll do iii. :) . Please why doesn't $f_{X}$ exist. – Godwin May 12 '11 at 17:49