Question: (12 points) Lab collaboration allowed Let X be the random variable whose PDF is given by fx (2) TT (1 + 2 2 ) for

(12 points) Lab collaboration allowed Let X be the random variable whose PDF is given by fx (2) TT (1 + 2 2 ) for x E R. Then X is a Cauchy random variable. (a) (3 points) Show that fx is a valid PDF; i.e. show ( fx(x)dx = 1. (b) (3 points) Find E[X]. (c) (3 points) Show that E[X2] = co. (d) (3 points) Find E[X3]

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