STA104/MTH135: Probability

Homework #6: Joint Distributions

Due: Friday, Oct 26

Text Problems are from Sheldon Ross, A First Course in Probability (6th/5th edns). 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. 290/293ff)
  

  6

  9

  20

  22

  28

  41

  42

• Exercise (p. 296/300ff)

  5

  (you do not have to evaluate the integral for XY, unless you're using Mathematica or Maple)
• 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!