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June 7th, 2013, 09:14 AM   #1
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What am I doing wrong? simple probability

Here's the question:

X and Y are discrete random variables that get values from 1 to N with equal probability. In other words, X and Y have a uniform distribution with values between 1 and N.
We defined another discrete random variable Z. Z=X-Y.
Find the probability function of Z.

My answer is incorrect, but I don't know why and I'd like an explanation. Here is my answer:

Z can get these values:

We can see that there are N-k events that yield X-Y=k, out of overall possible events.
This gives us that
But that is an incorrect answer. Why?
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June 7th, 2013, 01:11 PM   #2
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Re: What am I doing wrong? simple probability

Quote:
Originally Posted by OriaG
Here's the question:

X and Y are discrete random variables that get values from 1 to N with equal probability. In other words, X and Y have a uniform distribution with values between 1 and N.
We defined another discrete random variable Z. Z=X-Y.
Find the probability function of Z.

My answer is incorrect, but I don't know why and I'd like an explanation. Here is my answer:

Z can get these values:

We can see that there are N-k events that yield X-Y=k, out of overall possible events.
This gives us that
But that is an incorrect answer. Why?
When k < 0, you need to check your count.
Should be
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