But I think experimental proofs are kind of all you need for right now, using those simulations to show that they're really true. So it turns out that the variance of your sampling distribution of your sample mean is equal to the variance of your original distribution, that guy right there, divided by N. That's all it is. So if this up here has a variance of, let's say this up here has a variance of 20, I'm just making that number up, then, and then let's say your N is 20, then the variance of your sampling distribution of your sample mean for N of 20, well, you're just gonna take that, the variance up here, your variance is 20, divided by your N, 20. So here, your variance is going to be 20 divided by 20, which is equal to one. This is the variance of your original probability distribution, and this is your N. What's your standard deviation gonna be? What's gonna be the square root of that? Standard deviation is gonna be the square root of one, well, that's also going to be one.