10:I[6034,["878","static/chunks/9da6db1e-321469e27dc51aa4.js","954","static/chunks/d3ac728e-23c45ec216700eea.js","972","static/chunks/972-cf0c19383a04ee27.js","605","static/chunks/605-e6d88733e2ed50de.js","718","static/chunks/718-16004f17ca4d7da3.js","957","static/chunks/957-15c5f8c3ab68f8ee.js","34","static/chunks/34-c897dff191c58929.js","801","static/chunks/app/questions/%5Bslug%5D/page-d9aea32ec2d4c76b.js"],"default"] 11:I[8845,["878","static/chunks/9da6db1e-321469e27dc51aa4.js","954","static/chunks/d3ac728e-23c45ec216700eea.js","972","static/chunks/972-cf0c19383a04ee27.js","605","static/chunks/605-e6d88733e2ed50de.js","718","static/chunks/718-16004f17ca4d7da3.js","957","static/chunks/957-15c5f8c3ab68f8ee.js","34","static/chunks/34-c897dff191c58929.js","801","static/chunks/app/questions/%5Bslug%5D/page-d9aea32ec2d4c76b.js"],"default"] 5:["$","div",null,{"className":"min-h-screen bg-[#0f0f23]","children":[["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"Quiz\",\"name\":\"Math Question: Random Variables\",\"description\":\"Consider two independent variables X and Y with fX(x)=1 (0

Consider two independent variables XXX and YYY with fX(x)=1f_X(x)=1fX​(x)=1 (0<x<10<x<10<x<1) and fY(y)=2yf_Y(y)=2yfY​(y)=2y (0<y<10<y<10<y<1). What is the joint PDF fX,Y(x,y)f_{X,Y}(x, y)fX,Y​(x,y)?

Consider two independent variables $X$ and $Y$ with $f_X(x)=1$ ( $0<x<1$ ) and $f_Y(y)=2y$ ( $0<y<1$ ). What is the joint PDF $f_{X,Y}(x, y)$ ?