2 votes 2 votes Let the random variable X represent the number of times a fair coin needs to be tossed till two consecutive heads appear for the first time. The expectation of X is _______. Probability probability usergate2015 usermod expectation + – cocgame asked Jan 5, 2019 reopened Jul 9, 2022 by Arjun cocgame 3.8k views answer comment Share Follow See all 3 Comments See all 3 3 Comments reply PiratedVirus commented Jan 6, 2019 reply Follow Share https://gateoverflow.in/20011/tifr2011-a-6 0 votes 0 votes PiratedVirus commented Jan 6, 2019 reply Follow Share For more such problems: https://www.codechef.com/wiki/tutorial-expectation 0 votes 0 votes Alakhator commented May 14, 2019 reply Follow Share I think here the random variable concept is there. So I have provided my answer. Please correct me if I am wrong. 0 votes 0 votes Please log in or register to add a comment.
–1 votes –1 votes X= No of times coin is tossed. X=2,3,4.. X 2 3 4 5 ......... P[X=x] (1/2)^2 (1/2)^3 (1/2)^4 (1/2)^5 ......... E[x] = 2*(1/2)^2 + 3*(1/2)^3 + 4*(1/2)^4 + 5*(1/2)^5 + ..... This is an AGP. On solving this gives E[x] = 1.5 Alakhator answered May 14, 2019 Alakhator comment Share Follow See all 3 Comments See all 3 3 Comments reply shubham02 commented Jul 21, 2019 reply Follow Share where to learn the AP AND GP topic 0 votes 0 votes Ayan Kumar Pahari commented Feb 1, 2020 reply Follow Share It should be 6. 1 votes 1 votes shashankrustagi commented Sep 17, 2020 reply Follow Share 2(2^2-1) 1 votes 1 votes Please log in or register to add a comment.