Consider the family of pdfs indexed by the parameter 
, given by
where φ(x) and Φ(x) are respectively the pdf and cdf of a standard normal distribution.
(a) Clearly 
fo all x. Show that the pdf integrates to 1 over 
.
Next sketch the region of integration and then combine the integrands and use the polar coordinate transformation we used after expression (3.4.1).