STA104/MTH135: Probability

Homework #6: Joint Distributions

Due: Thursday, Oct 23

Text Problems are from Sheldon Ross, A First Course in Probability (6th edn). I urge you to use Mathematica or Maple to do the integrals, unless you are a masochist. For example, the double-integrals needed to solve one of the problems below can be evaluated in
Mathematica with the command Integrate[ Integrate[ y(6/7)(x^2+x*y/2),{x,0,1} ], {y,0,2} ] , or in
Maple with the command int( int(y*(6/7)*(x^2+x*y/2), x=0..1), y=0..2); .

• Problems (pp. 290ff)
  9 13 16 24 32 50 54
• Exercise (p. 296ff)

  8

• Another Problem
  Drop three quarters (diameter: 1") into an empty Family Size Campbell's Cream of Mushroom Soup can (diameter: 5"). Find the probability distribution for the distance from the center of the can bottom to the center of the farthest coin (the one closest to the edge of the can). What assumptions did you make?

Good Luck!