https://file.aiquickdraw.com/mathbot/file/1726314736782hqgq4xit.jpg

It looks like the image contains mathematical notation. Upon reviewing it, here’s the transcription of the equation:

\[
\frac{1}{\sqrt{2\pi} \sigma} e^{-\frac{(x-\mu)^2}{2\sigma^2}}
\]

This is the probability density function (PDF) of a normal distribution, often referred to as the Gaussian function. It describes the bell-shaped curve in statistics:

- \( \mu \) is the mean or expectation of the distribution.
- \( \sigma \) is the standard deviation (a measure of spread or dispersion).
- \( \pi \) is the constant pi, approximately 3.14159.
- \( e \) is Euler's number, approximately 2.71828, used in exponential functions.

Would you like further details on how this formula is used, or any questions about the normal distribution?

Here are 5 related questions to expand on this:

1. What is the significance of the mean (\( \mu \)) in a normal distribution?
2. How does the standard deviation (\( \sigma \)) affect the shape of the normal curve?
3. Can you explain how the area under the curve relates to probability?
4. What is the central limit theorem, and how does it relate to the normal distribution?
5. How can you calculate the probability of an event using this probability density function?

**Tip:** In the normal distribution, approximately 68% of the data falls within one standard deviation (\( \sigma \)) from the mean, and 95% within two standard deviations.

What does the equation represent, and how is it used?

Explore the normal distribution's formula and its significance in probability theory and statistics. Learn how the Gaussian function is applied, including the importance of the mean (μ), standard deviation (σ), and its relationship with the Central Limit Theorem.

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