Mathematica Simulating Normal Distribution in Mathematica: Histogram and PDF Plotting

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To simulate a normal distribution in Mathematica using the central limit theorem, one can sum multiple uniform random variables generated by RandomReal[]. To visualize the results, it's essential to plot both the histogram of the generated data and the Gaussian probability density function on the same graph. The key to achieving this is using the Show function, which allows for the combination of multiple graphics elements. An example command is provided, demonstrating how to overlay a histogram of normally distributed random variables with a separate plot, although the example incorrectly uses Sin[x] instead of the Gaussian function. Correcting this will yield the desired visualization of the normal distribution alongside the histogram.
Sam_Goldberg
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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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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}]]
 

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