An archive the questions from Mark's Fall 2018 Stat 225.

Independence test for continuous, jointly distributed random variables

Mark

Suppose that X and Y have joint distribution over [0,1]\times[0,1]

f(x,y) = c(x^2 +xy + y^3),

where c is chosen to make this a good probability density function.

  1. Find c.
  2. Evaluate E(X), E(Y), and E(XY).
  3. Determine if X and Y are independent.
megan
  1. c = \frac{6}{5}
  2. E(X)=\frac{13}{20}, E(Y)=\frac{16}{25}, E(XY)=\frac{121}{300}
  3. X and Y are not independent.