Assume (x,Y) is a continuous bivariate random variable with the joint probability density function (PDF): f_(x,Y)(x,y)={(0.5,|x|+|y|<1,),(0, otherwise. ):} Here, |z| is the absolute value of z : |z|={(z,z>=0,),(-z.,z<0.):} (a) Find the marginal PDF of x . (b) Define Z=x+Y . Find the cumulative distribution function (CDF) of Z . Name the distribution of Z and its parameters. (c) Now define W=|x|+|Y| . Find the CDF of W . Find the mean E(W) .

Assume (x,Y) is a continuous bivariate random variable with the joint probability density function (PDF): f_(x,Y)(x,y)={(0.5,|x|+|y|<1,),(0, otherwise. ):} Here, |z| is the absolute value of z : |z|={(z,z>=0,),(-z.,z<0.):} (a) Find the marginal PDF of x . (b) Define Z=x+Y . Find the cumulative distribution function (CDF) of Z . Name the distribution of Z and its parameters. (c) Now define W=|x|+|Y| . Find the CDF of W . Find the mean E(W) .