STAT 333 Winter 2010 Test 1 SOLUTIONS
Thurs, Feb 11 4:00 5:30 pm
First (given) name:_ Last (family) name:_
Student ID #:_ UW userid:_
Instructions: 1. 2. 3. 4. 5. 6. Please fill in the above information This test has 6 pages, including this cover page Ans
STAT 333 Winter 2010 Test 2 SOLUTIONS
Thurs, March 18, 4:00 5:30 pm
First (given) name:_ Last (family) name: _
Student ID #:_ UW userid:_
Instructions: 1. 2. 3. 4. 5. 6. Please fill in the above information This test has 7 pages, including this cover page
Stat 333 Winter 2007
Solutions: Generating Functions
#1 (a)
n=0
n5 sn . Use a ratio test (other tests are also possible). (n + 1)5sn+1 n+1 5 lim lim | |( |= ) s| = |s| n n n5 s5 n So this limit is < 1 i |s| < 1 i.e. converges for |s| < 1
(b)
n=0
1 sn = (
Gamblers Ruin Derivation and Example Suppose a gambler starts with $i and wins or loses $1 on each game. P(win) = p , P(lose) = 1 p = q. They will stop if they go bankrupt or if they reach $k. Let Pi = P(gambler reaches $k before going bankrupt, given the