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# ﻿Assume (x,Y) ﻿is a continuous bivariate random variable with the joint probability density function (PDF):

﻿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) .

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