SFSU Physics and Astronomy Department

Ph 490 Problem Set 1

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Ref: Bevington, 3rd ed, p. 28

Problem 1. For the Gaussian probability distribution,

(a) Show that, for the distribution to be normalized, the factor A must have the value

(b) Show that the mean of the distribution is equal to m, and that the standard deviation of the distribution about the mean is equal to s.

Problem 2. Use the general rule for error propagation for functions f(x) of a single variable x,

,

to prove the following rule of error propagation for a power-law function.

If x is a random variable with standard deviation s_x, then the function of x

has standard deviation s_f given by

.

2/7/2004 10:38 AM