# Cumulative Distribution function

• Mar 17th 2011, 02:08 PM
stordase39
Cumulative Distribution function
Lets say I have a random variable X that can take values 1,2,3,4 and 5 with probabilities 0.2 0.3 0.1 0.25 0.10 0.05.

My question is how I can determine the Cumulative distribution function and how I can use it to generate the numbers from X?
• Mar 17th 2011, 02:27 PM
pickslides
You have five values and six probabilities.
• Mar 17th 2011, 02:41 PM
Plato
Quote:

Originally Posted by stordase39
Lets say I have a random variable X that can take values 1,2,3,4 and 5 with probabilities 0.2 0.3 0.1 0.25 0.10 0.05.

My question is how I can determine the Cumulative distribution function?

I will get you started on the CDF:
$\[
P\left( {X \leqslant b} \right) = F(b) = \left\{ {\begin{array}{rl}
{0,} & {b < 1} \\
{0.2,} & {1 \leqslant b < 2} \\
{0.5,} & {2 \leqslant b < 3} \\
{?,} & {3 \leqslant b < 4} \\
?, & ? \\
?, & ? \\ \end{array} } \right.$
• Mar 18th 2011, 01:18 AM
stordase39
Ok sorry for that... say that the probabilities are 0.2 0.3 0.1 0.1 0.3 then. How can i generate numbers from that distribution using the CDF.
• Mar 18th 2011, 03:43 AM
mr fantastic
Quote:

Originally Posted by stordase39
Ok sorry for that... say that the probabilities are 0.2 0.3 0.1 0.1 0.3 then. How can i generate numbers from that distribution using the CDF.

Read post #3. Learn from it. Post all your work and say where you get stuck.
• Mar 18th 2011, 04:05 AM
stordase39
Quote:

Originally Posted by mr fantastic
Read post #3. Learn from it. Post all your work and say where you get stuck.

I know how to contruct the CDF now. My question is how to generate numbers from the distribution using the CDF?
• Mar 18th 2011, 04:26 AM
Plato
Quote:

Originally Posted by stordase39
I know how to contruct the CDF now. My question is how to generate numbers from the distribution using the CDF?

What do you mean by that question?
What numbers?
• Mar 18th 2011, 02:24 PM
mr fantastic
Quote:

Originally Posted by Plato
What do you mean by that question?
What numbers?

I'm inclined to suggest to the OP that s/he make a spinner, with the area for each number weighted according to the probability of that number occuring.

Memo to OP: The usefulness of the help you get is directly proportional to the accuracy and clarity of the question you post.
• Mar 19th 2011, 12:12 AM
CaptainBlack
Quote:

Originally Posted by Plato
What do you mean by that question?
What numbers?

I think what he means is: Given a RV $X \sim U(0,1)$ find a transformation $f(.)$ such that $Y=f(X)$ has the required distribution?

$y=F^{-1}(x)$