1. F(x) = 1 - 1/x (x greater than or equal to 1)
You can do this in two ways. You can calculate the PDF,
f, and then integrate
. The PDF is just the derivative of the CDF, if continuous.
which does not converge.
2. F(x) = 1 - exp(-x^2) (x greater than or equal to 1)
Mr F says: Small typo here. Should be 2x, not -2x .... The bigger problem is that it's not actually a valid cdf .... The support should be [0, +oo), NOT [1, +oo).
I guess I would try integration by parts with
You will probably need to use the standard normal table in your stats book to do
which should pop out after the integration by parts step. That integral is almost the area under the curve of the standard normal distribution, but it is missing a
.