# How to show variance increases in an open system vs. a closed system?

Lets says I have 10 dogs and 1000 grams of premium dog food. I unleash said dogs in a room with said 1000 grams of dog food, weighing them before the experiment and then weighing them once more after the experiment is over. Assuming they consume all the dog food and do not burn a lot of calories, urinate or defecate during this exercise we expect each dog to gain 100 grams of weight in average.

So statistically the expectancy of the weight gain (with abstract dogs in a hypothetical world) would be 100 grams per dog.

Now, if I only weigh 9, 8 or i 9 random dogs out of the 10 dogs we started with, the average weight gain will vary. Assuming normal distribution and the constrains of the system, how would I calculate the increasing variance for i < 10 dogs for each i?

No dogs were harmed in the making of this question.

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