Let X1 and X2 be independent, each having a standard normal distribution. The pair (X1, X2)…
Let X1 and X2 be independent, each having a standard normal distribution. The pair (X1, X2) corresponds to a point in a two-dimensional coordinate system. Consider now changing to polar coordinates via the transformation, Let X1 and X2 be independent random variables, each having a standard normal distribution. Show that the pdf of the ratio Y = X1/X2 is given by f( y) = 1/[π(1 + y2 )] for -∞ 1 < y="">< 1.="" (this="" is="" called="" the="" standard="" cauchy="" distribution;="" its="" density="" curve="" is="" bell-shaped,="" but="" the="" tails="" are="" so="" heavy="" that="" μ="" does="" not=""> Apr 08 2022 03:22 PM
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