An essential function in statistics and the study of the normal distribution is the error function a.

Question:

An essential function in statistics and the study of the normal distribution is the error function

х 2 erf (x) dt. TT

a. Compute the derivative of erf (x).

b. Expand e^-t2 in a Maclaurin series; then integrate to find the first four nonzero terms of the Maclaurin series for erf.

c. Use the polynomial in part (b) to approximate erf (0.15) and erf (-0.09).

d. Estimate the error in the approximations of part (c).

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