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Randomly Generated Normal PDF

Randomly Generated Normal PDF
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2016-01-14 06:50
FunctionCalculusIntegralProbability & StatisticsTransformation
This example demonstrates the random generation of a Normal Probability Density Function (PDF). Key math concepts include Normal Distribution, PDF, Step Functions, Calculus, Integral Calculus. The construction uses commands like Integral, Segment, RandomUniform, Normal, RandomNormal, and objects such as mean, stdev, q, a, b, text1, text2, text3, μ, A, c, B, C, mu, sigma, f, mu1, sigma1, g, mu2, sigma2, h. Suitable for high school and above students to understand the properties and calculations of Normal Distributions.

GeoGebra Commands & Parameters

  1. Integral(q, mean - (5 * stdev), mean + (5 * stdev)) → a
  2. Integral(q, mean - stdev, mean + stdev) → b
  3. Segment(A, μ) → c
  4. RandomUniform(-4, 4) → mu
  5. RandomUniform(0.2, 3) → sigma
  6. Normal(mu, sigma, x) → f
  7. RandomUniform(-4, 4) → mu1
  8. RandomUniform(0.1, 2) → sigma1
  9. Normal(mu1, sigma1, x) → g
  10. RandomNormal(0, 1) → mu2
  11. RandomNormal(0, 2) → sigma2
  12. Normal(mu2, sigma2, x) → h

AI Drawing Prompt Reference

Draw a graph of a normal probability density function, showing randomly generated mean and standard deviation, including the integral area over the range of mean ± 5 standard deviations, and two normal distribution curves with different parameters, connecting the mean point with a line segment to illustrate the randomness and integral properties of the normal distribution.
The prompt above was compiled from the original drawing commands and is for reference only.