The following distribution 7(x|o,q) 2(202)/4r(1/9) is a generalization of the univariate Gaussian distribution, where I denotes the Gamma function (see https://en.wikipedia.org/wiki/Gamma_function for details, but you only need to know r(1/2) = 7 for this problem). Show that this distribution reduces to the Gaussian distribution when q = 2. Consider a regression model in which that target variable is given by t = y(x, w) + and e is a random noise variable drawn from the distribution (2). Show that the log likelihood log (tx, w, ) = Al 681-001 CS 695-001 | Assignment 1 Fall 2022 function over w and , for an observed data set of input vectors x = [x,...,xN] RN and corresponding target variables t = [t...,tN] RN, is given by 202 -exp(- 1 N N y(x, w) -til-log(20) + cst, 9 i=1 where 'cst' denotes terms independent of both w and . The following distribution 7(x|o,q) 2(202) /4r(1/9) is a generalization of the univariate Gaussian distribution, where I denotes the Gamma function (see https://en.wikipedia.org/wiki/Gamma_function for details, but you only need to know r(1/2) = for this problem). Show that this distribution reduces to the Gaussian distribution when q = 2. Consider a regression model in which that target variable is given by t = y(x, w) + and e is a random noise variable drawn from the distribution (2). Show that the log likelihood -exp(- 1 Al 681-001 CS 695-001 | Assignment 1 Fall 2022 function over w and , for an observed data set of input vectors x = [x,...,XN] RN and corresponding target variables t = [,...,t] RN, is given by log (tx, w, ) = N N 202 ly (x, w) -t-log(20) + cst, i=1 9 where 'cst' denotes terms independent of both w and .