Question: You are given X and Y as two jointly continuous random variable with their joint PDF as below: (include the calculations) f X , Y

You are given X and Y as two jointly continuous random variable with their joint PDF as below: (include the calculations)

f X , Y ( x , y ) = { c y 3 + 2 x 2 + 1 , 0 x , y 1 (when x, y are between 0 - 1, this is their joint PDF and it is 0 otherwise)

  1. Find the constant C (5 points)
  2. Find the marginal PDF for x and y (9 points)
  3. Find P ( 0 X , Y 0.25 ) (5 points)
  4. Find E [ X 2 Y ] (9 points)

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