Chapter 17 Random Variables616
Homework Problems
Problem 17.17.
A coin will be flipped repeatedly until the sequence tail/tail/head (TTH) comes
up. Successive flips are independent, and the coin has probabilitypof coming up
heads. LetNTTHbe the number of coin tosses untilTTHfirst appears. What value
ofpminimizes ExŒNTTHç?
Homework Problems
Problem 17.18.
LetRandSbe independent random variables, andfandgbe any functions such
that domain.f /Dcodomain.R/and domain.g/Dcodomain.S/. Prove thatf.R/
andg.S/are independent random variables. Hint:The eventŒf.R/Daçis the
disjoint union of all the eventsŒRDrçforrsuch thatf.r/Da.