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Assume that X and Y has a continuous joint p.d.f. as (28x^2)*(y^3) in 0<y<x<1 interval. Otherwise...

Assume that X and Y has a continuous joint p.d.f. as (28x^2)*(y^3) in 0<y<x<1 interval. Otherwise the joint p.d.f. is equal to 0.

  1. Prove that the mentioned f(x,y) is a joint probability density function.
  2. Calculate E(X)
  3. Calculate E(Y)
  4. Calculate E(X2)
  5. Calculate Var(X)
  6. Calculate E(XY)
  7. Calculate P(X< 0.1)
  8. Calculate P(X> 0.1)
  9. Calculate P(X>2)
  10. Calculate P(-2<X<0.1)
Math   Statistics-And-Probability   
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