standard deviation

Suppose that we are interested in diffusion in the x direction and that some property is suddenly injected into a gas at point x0, in such a way that its initial density function is given by Q(x, t = 0) = Q0d(x – x0). Diffusion causes it to spread out with time. In terms of the diffusion constant D:
(a) How does the width of the spread, as measured by the standard deviation s, vary with time?
(b) How does the concentration at point x = x0 vary with time?

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