# The plot thickens - Solution

The probability density function of the normal or Gaussian distribution, is:y(t)=(1/(sigma*(2*pi)^0.5))*e^(-0.5*((t-mu)/sigma)^2)

where mu is the mean and sigma the standard deviation.

## y(t) and amplitude spectrum with mu=0 sigma=0.05

## y(t) and amplitude spectrum with mu=0 sigma=0.1

## y(t) and amplitude spectrum with mu=0 sigma=0.5

Notice that the spread of frequencies has narrowed as as the spread of the original function has increased.

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