MathJax(?): Can't find handler for document MathJax(?): Can't find handler for document Let Ч and Y be absolutely continuous and discrete random variables, respectively. Does random vector ( X , Y ) have to be absolutely continuous with respect to the product measure on the respective supports of Ч and Y?I think this is true because the following equality holds

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MathJax(?): Can&#039;t find handler for document MathJax(?): Can&#039;t find handler for document Let   Ч and   Y be absolutely continuous and discrete random variables, respectively. Does random vector   (  X  ,  Y  ) have to be absolutely continuous with respect to the product measure on the respective supports of   Ч and   Y?I think this is true because the following equality holds

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MathJax(?): Can&#039;t find handler for document MathJax(?): Can&#039;t find handler for document assuming  &amp;#x2200;      x    0    ,  &amp;#x2203;      y    0    &amp;#x2260;      y    1    ,  &amp;#x2203;      &amp;#x03F5;    0    :      |    f  (      y    0    )  &amp;#x2212;  f  (      y    1    )      |    &amp;gt;      &amp;#x03F5;    0    &amp;#xA0;  =&amp;gt;  &amp;#xA0;      |        f          X      ,      Y        (      x    0    ,      y    0    )  &amp;#x2212;      f          X      ,      Y        (      x    0    ,      y    1    )      |    &amp;gt;      &amp;#x03F5;    0  example:   X is normal and   Y  &amp;#x223C;  B  e  r  n  o  u  l  l  i  (  0.5  ) then       f          X      ,      Y        (  0  ,  0  )  =      f    X    (  0  )  &amp;#x2217;  0.5 and       f          X      ,      Y        (  &amp;#x03F5;  ,  0  )  =  0

Let Ч and Y be absolutely continuous and discrete random variables, respectively. Does r

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