Conditional expectation coin toss problem
So i have this question: "Consider two independent tosses of a biased coin, which lands heads up with probability 2/3. Suppose you win/loose $1 whenever the coins lands heads/tails up. Let X1 and X2 denote your cumulative winnings after 1 respectively 2 tosses. - CALCULATE the conditional expectation E(X1|X2)"
I have tried to make X1 & X2 table, then find out f (X1|x2), and then the expectation.. but lack of routine with this kind of calculations makes me confused. Thank you.
Re: Conditional expectation coin toss problem
As it sounds like you have spotted; there are only 4 possible let outcomes (ww ll wl lw). work out the probability of each and the associated values of x1 and x2. I combine these to get the joint distribution of x1&x2 and you should be able to do the rest