So in the past, I’ve been pretty happy with my self-awareness level. It was at about 12 or so. I’ve been at about a seven since then. I think my self-awareness level has taken a little dip with the increase in my anxiety. I’m not going to lie, I haven’t taken a break, but I have not been to sleep either. I try to keep myself busy but not to the point of exhaustion.
The standard deviation of the distribution of a random variable is a measure of the spread of that distribution. When someone says that the standard deviation of a random variable is the measure of the spread of that random variable, they really mean that the standard deviation represents the spread of a random variable that is normally distributed.
The spread of a normal random variable is usually expressed as the square root of the variance. For a normal distribution, the square root of the variance is called the standard deviation. The standard deviation is a measure of how far apart the values of the random variable are from each other. If we take a square root of the variance of a normal random variable, we get a standard deviation of 1.
The square root of a random variable is exactly one, but for a normal distribution it’s quite large. It’s like we’re in a room with ten people that are all having a conversation in a row.
Of course, if we take a square root of a standard deviation we get a standard deviation of 10. A normal distribution has a standard deviation of 10. The square root of 10 is really quite big and has a huge meaning. It’s a very special and important number.
The square root of 10 is the square root of a 1,000,000 times larger number that in any way resembles a real random variable. This is a number that is 10 to the power of 10,000,000. The square root of 10 to the power of 10,000,000 is 100 million. This is a very big number that is 100 million times that of a 1,000,000. That is 10 to the power of 10,000,000.
So 100 million is a very big number, but 10 to the power of 1,000,000 is just 10.
This is one of the biggest numbers you will ever see in a math course, but the square root of 100 million is just 10.
The square root of 100 million is just 10 and that is pretty huge. So 10 to the power of 10,000,000 is definitely one of the biggest numbers you will ever see. But 10 to the power of 1,000,000 is just 10, so it’s not that big of a number in and of itself. But it’s still one of the biggest numbers that you will ever see.
What’s even more interesting is that its a number that we can use in a real world context to talk about things like statistical significance. Think about how many times you hear a statistical number like “10 to 60” and you’re instantly thinking, “Oh, you know, that’s huge, but it’s just 10, so it doesn’t really mean anything.