# Thread: Three (or more) normally distributed variables

1. ## Three (or more) normally distributed variables

Hi
I have three variables, X, Y and Z with all different means but same standard deviation. All are normally distributed. It could be four in some cases.

How can I calculate probability that a random observation on X will be > than Y and Z?

I appreciate any kind of help. I will perform test in Excel so extra good with some excel tip.

2. ## Re: Three (or more) normally distributed variables

Thinking of it.. variables are more likely to be Poisson distributed.. Could I apply Skellam distribution here in some way?

I dont have observations for these variables. X, Y and Z are estimated number of goals in three different independent football matches. I would like to calculate probability that it will be most goals in Match X.

3. ## Re: Three (or more) normally distributed variables

If they have different means but the same standard deviation how could they be poisson?

4. ## Re: Three (or more) normally distributed variables

that makes of course no sense

What I am trying to do is to estimate probability that Match A will contain most goals among Match A, B and C.

My first idea was to see number of goals as normally distributed with estimated variance from 4K matches. Match A, B and C will have different estimations for number of goals.

The variable of interest here is number of Goals, X. That will come from three different populations, match A, B and C.

That is probably a better way to describe what im trying to do. But how should I see X distributed? And how can I calculate probability that Match A will contain most goals?

Mean for goals scored in 4K matches = 2.74 and variance = 2.9. So I dont think there will be any problem with over dispersion, in this case if I view X as Poission distributed.

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