# Thread: Variance of two deterministic distributions

1. ## Variance of two deterministic distributions

I would like to know the variance of two deterministic distributions when putting them together.

Of course the variance of the two seperate deterministic distributions is zero, right?

I have a machine that processes products and with chance x it processes product A and with chance 1-x it processes product B, so the chances are known.

What will be the variance of the processing time of the machine?

Thank you in advance!

2. ## Re: Variance of two deterministic distributions

http://en.wikipedia.org/wiki/Varianc...andom_variable

In particular you may take a look at the Bernoulli distribution which take values :

http://en.wikipedia.org/wiki/Bernoulli_distribution

3. ## Re: Variance of two deterministic distributions

Originally Posted by BGM
http://en.wikipedia.org/wiki/Varianc...andom_variable

In particular you may take a look at the Bernoulli distribution which take values :

http://en.wikipedia.org/wiki/Bernoulli_distribution
Thank you I understand it.

My p will be then r/(r+r/t), I can fill that in in the formula for the variance p(1-p). But, in the bernoulli distribution, the values are 0 or 1 and in my assignment this is between different numbers, and I think that these numbers influence the variance. Is that true? So, do I have to convert the variance formula with my other values? And so, how?

4. ## Re: Variance of two deterministic distributions

Let say you have a discrete random variable with only 2 support points

And you correctly obtain that .

So you look at the formula I posted before. To use it you need to calculate

first.

Then use either version of it will do.

5. ## Re: Variance of two deterministic distributions

Originally Posted by BGM
Let say you have a discrete random variable with only 2 support points

And you correctly obtain that .

So you look at the formula I posted before. To use it you need to calculate

first.

Then use either version of it will do.
OK, I have now calculated E [X] andE [X] ^2. And then variance = E [X] ^2 - E [X].
Now I need de covariation coefficient. I wonder if it is simply my E [X]/variance, or something else because it is a discrete distribution?

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