SERVING THE QUANTITATIVE FINANCE COMMUNITY

 
User avatar
RoniNYC
Topic Author
Posts: 18
Joined: September 6th, 2011, 11:25 pm

Expected value of Tosses to get THH

April 23rd, 2013, 12:39 am

I know how to solve this problem using Markov Chain and I get 8.However, I'm trying to solve it using expected values, and I can't get it...If I were to look for HHH, I would do it this wayLet X=expected number of tosses to get HHHX=(1/8)*3+1/8*(3+X)+1/2*(1+X)+1/4*(2+X) And, I would get 14....Now, in the 'THH' case, the process doesn't always goes to the origin, so it much take fewer tosses... anybody know how I can adjust the expected value equation?
 
User avatar
Peniel
Posts: 59
Joined: April 8th, 2006, 9:46 am

Expected value of Tosses to get THH

April 23rd, 2013, 6:32 am

<wrong>
Last edited by Peniel on April 22nd, 2013, 10:00 pm, edited 1 time in total.
 
User avatar
deimanteR
Posts: 48
Joined: February 5th, 2013, 11:26 am

Expected value of Tosses to get THH

April 23rd, 2013, 7:20 am

QuoteOriginally posted by: RoniNYCNow, in the 'THH' case, the process doesn't always goes to the origin, so it much take fewer tosses... anybody know how I can adjust the expected value equation?When conditioning on the first outcome you need to solve for the intermediate quantity E X_T - the expected outstanding number of tosses after having thrown T in the first one. That's easy: x = 1 + (1/2) E X_T + (1/2) xHence E X_T = x -2. Here x is the expectation you are looking for. Now condition on the second and the third toss using the above result (sinse wrong outcome gives the first element to your sequence). This yields x = 8.
 
User avatar
Peniel
Posts: 59
Joined: April 8th, 2006, 9:46 am

Expected value of Tosses to get THH

April 23rd, 2013, 12:35 pm

For completeness, with E=E X_T:E = (1/4)*2 + (2/4)*(E+2) + (1/4)*((1/2)*3 + (1/2)*(E+3)) -> E=6 -> x=8
 
User avatar
RoniNYC
Topic Author
Posts: 18
Joined: September 6th, 2011, 11:25 pm

Expected value of Tosses to get THH

April 25th, 2013, 4:28 pm

Makes sense... thanks guys.
ABOUT WILMOTT

PW by JB

Wilmott.com has been "Serving the Quantitative Finance Community" since 2001. Continued...


Twitter LinkedIn Instagram

JOBS BOARD

JOBS BOARD

Looking for a quant job, risk, algo trading,...? Browse jobs here...


GZIP: On