Problems (p171-180): 66, 73, 74, 77; (p228-231) 3, 4, 10, 13, 23, 32, 39.
Theoretical exercises (p232-235): 9, 14.
Bonus questions (Due Thu, Nov 6):
1. A uniform distribution on a sphere is a distribution that assigns equal probability to sets of equal volume (much like a uniform distribution on an interval assigns equal probability to intervals of equal length). Let U=(x,y,z) be a uniform random variable on a sphere of radius r centered at the origin and let D be its distance from the origin. Find the cdf and the mean of D.
2. Show by counterexample that marginally continuous random variables are not necessarily
jointly continuous.