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Stuck on a statistics problem - probability distribution

post #1 of 6
10/24/10 at 1:57pm
Thread Starter 

Anyone good with statistics here?  I'm stuck on a problem.  The question is: 

 

Random variable X is a continuous variable formed by the sum of two random numbers between 0 and 1. 

a) Draw the probability distribution of X. 

b) Verify using geometry that the area under the curve is 1. 

c) What is the probability that X is less than 0?  [the answer to this is zero probability because X is formed by the sum of two positive numbers]

d) What is the probability that X is greater than 0.5?  [need to know the answer to part A to get this]

 

Here's what I know: 

The minimum value of X is 0 and the maximum is 2.  

There is only one way to form X = 0, when both numbers are 0. 

There is only one way to form X = 2, when both numbers are 1. 

 

Any help would be appreciated. 

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post #2 of 6
10/24/10 at 3:05pm
Quote:
Originally Posted by lmf22 View Post

Anyone good with statistics here?  I'm stuck on a problem.  The question is: 

 

Random variable X is a continuous variable formed by the sum of two random numbers between 0 and 1. 

 

...

 

What's the distribution of these two random numbers? e.g. are they iid U(0,1) or something else?

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post #3 of 6
10/24/10 at 4:03pm

*Deleted content due to misunderstanding of the question*


Edited by Exediron - 10/24/10 at 4:18pm
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post #4 of 6
10/24/10 at 6:28pm

The probabnility of me helping solve this problem is nil.

 

Send Tom (nattonrice) a pm.  He's a Ph.D student in maths.


Edited by wink - 10/24/10 at 6:29pm
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post #5 of 6
10/24/10 at 6:48pm


 

Quote:
Originally Posted by lmf22 View Post

Anyone good with statistics here?  I'm stuck on a problem.  The question is: 

 

Random variable X is a continuous variable formed by the sum of two random numbers between 0 and 1. 

a) Draw the probability distribution of X. 

b) Verify using geometry that the area under the curve is 1. 

c) What is the probability that X is less than 0?  [the answer to this is zero probability because X is formed by the sum of two positive numbers]

d) What is the probability that X is greater than 0.5?  [need to know the answer to part A to get this]

 

Here's what I know: 

The minimum value of X is 0 and the maximum is 2.  

There is only one way to form X = 0, when both numbers are 0. 

There is only one way to form X = 2, when both numbers are 1. 

 

Any help would be appreciated. 



When you say "random number between 0 and 1" you mean that the number is uniformly distributed between 0 and 1 right? In other words, the probability of the number being in a certain interval is proportional to the length of the interval. If you're not sure then this is what it means...I've seen textbooks that write this.

 

There are a few more problems with the question: 

A) Are you supposed to plot the density (pdf) or distribution (cdf)? I ask because..

B) The area under the distribution is not supposed to be equal to 1. The area under the density is equal to 1.

 

You probably need to know that X is the sum of 2 independent random variables (although this may be implicitly assumed). Otherwise you can't answer the question.

 

As a hint: It's a conditional probability question.


Edited by XXII - 10/24/10 at 6:56pm
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post #6 of 6
10/25/10 at 12:01am

Well if it's Uniform(0,1) refer to the maths below.

 

If the 2 random numbers are not uniformly distribution, please inform us what their distribution is.

 

 

Let A, B be the two 'random numbers' such that A, B iid U(0,1)

 

If X = A + B, then

 

           x         0<x<=1

f(x) =  2-x      1<x<=2

          0          otherwise

 

 

You should be able to use that to draw your pdf/cdf, and work out your probabilities, etc.

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