Cumulative Distribution function

**stordase39** · March 17th 2011, 01:08 PM

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?

**pickslides** · March 17th 2011, 01:27 PM

You have five values and six probabilities.

**Plato** · March 17th 2011, 01:41 PM

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.$

**stordase39** · March 18th 2011, 12:18 AM

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.

**mr fantastic** · March 18th 2011, 02:43 AM

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.

**stordase39** · March 18th 2011, 03:05 AM

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?

**Plato** · March 18th 2011, 03:26 AM

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?

**mr fantastic** · March 18th 2011, 01:24 PM

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.

**CaptainBlack** · March 18th 2011, 11:12 PM

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?

The answer required is then:

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

CB

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