Simulating Normal Distribution in Mathematica: Histogram and PDF Plotting

In summary, a normal distribution is a bell-shaped curve that is symmetrical around the mean and is commonly used to describe real-world phenomena. In Mathematica, you can simulate a normal distribution using the <code>RandomVariate</code> function and create a histogram of the data points using the <code>Histogram</code> function. You can also plot the probability density function using the <code>Plot</code> function and compare two distributions using the <code>Show</code> function and statistical tests.
  • #1
Sam_Goldberg
46
1
Hi guys,

On my homework, I'm simulating a normal distribution on Mathematica by adding up a bunch of RandomReal[] , that is, uniform(0,1) random variables, and using the central limit theorem. I would like to plot both the histogram and the actual Gaussian probability density function on the same graph, but it does not seem that I'm able to use both the Histogram and Plot functions at the same time. How should I do this? Thanks.
 
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  • #2
You use "Show" to show multiple graphics at a time:

Show[Histogram[RandomReal[NormalDistribution[0, 1], 200]], Plot[Sin[x], {x, -6 Pi , 6 Pi}]]
 

1. What is a normal distribution?

A normal distribution, also known as a Gaussian distribution, is a statistical distribution that is often used to describe real-world phenomena. It is a bell-shaped curve that is symmetrical around the mean, with most data points falling near the mean and fewer data points falling further away from the mean. Many natural and human-made processes follow a normal distribution, making it a widely used and important tool in statistics.

2. How do you simulate a normal distribution in Mathematica?

In Mathematica, you can simulate a normal distribution by using the built-in function RandomVariate. This function takes the distribution you want to simulate as an argument, in this case NormalDistribution, and generates a random sample of data points that follow that distribution. You can specify the mean and standard deviation of the distribution to customize the simulation.

3. How do you create a histogram of a simulated normal distribution in Mathematica?

To create a histogram of a simulated normal distribution in Mathematica, you can use the Histogram function. This function takes a list of data points as its input, so you will need to first use RandomVariate to generate the data points. You can also specify the number of bins and other options to customize the appearance of the histogram.

4. Can you plot the probability density function (PDF) of a simulated normal distribution in Mathematica?

Yes, you can plot the PDF of a simulated normal distribution in Mathematica using the Plot function. This function takes an expression or function as its input, so you can use the built-in function PDF to calculate the PDF of the normal distribution. You can also specify the range of values to be plotted and other options to customize the appearance of the plot.

5. How can I compare two simulated normal distributions in Mathematica?

To compare two simulated normal distributions in Mathematica, you can plot them on the same graph using the Show function. This function takes multiple plots as its input and combines them into a single graph. You can also use different colors or styles for each plot to make them easier to distinguish. Additionally, you can use statistical tests such as the Mean or StandardDeviation functions to compare the summary statistics of the two distributions.

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