I want to plot the following Gaussian function
Is there a way that I can do this symbolically without giving values to the constants.
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$\begingroup$ Short answer is no, but you could do e.g. a contour plot with x on the x axis and b on the y axis? $\endgroup$– chrisCommented Oct 14, 2020 at 10:29
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3$\begingroup$ Well, you could put $\hat{f} = f/a$ and $\hat{x} = (x - b)/c$, giving the "universal" curve $\hat{f} = \exp(-\hat{x}^2 / 2)$. The three constants just change the vertical scale, the horizontal offset, and the horizontal scale of the curve. $\endgroup$– yawnocCommented Oct 14, 2020 at 13:06
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1 Answer
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How about this?
f[x_, a_, b_, c_] = a PDF[NormalDistribution[b, c], x]
Then
ContourPlot3D[f[x, 1, b, c], {x, -3, 3}, {b, -1, 1}, {c, 1, 2}]
Note that I am not claiming it is particularly informative!
This might be more useful?
Plot[Table[f[x, 1, b, 1], {b, -1, 1, 1/4}] // Evaluate, {x, -2, 2},
PlotStyle -> ColorData[10]]
Plot[Table[f[x, 1, 1/2, c], {c, 1/2, 2, 1/4}] // Evaluate, {x, -2, 2},
PlotStyle -> ColorData[10]]
