I have this question that I don't know where to begin, any help will be greatly appreciated.
Consider the following random experiment. Toss a coin until the same number of heads and tails have been observed. Take as random variable, X, the observed number of heads (or tails). Determine the first few values in the probability distribution and calculate
$\sum^{5}_{n=1} nP (X = n)$
I'm not sure exactly where to start, if someone could point me in the right direction that would be great! thanks
Since we don't differentiate between $H$ and $T$, denote the fist tossed coin $\alpha$, because it doesn't matter what you've tossed. Then you're either done w.p $\frac{1}{2}$ by tossing $\alpha^c$ (NOT alpha) or you return to the state $\alpha$ w.p. $\frac{1}{2}$. Hence you get $P(X=1)$ w.p. $\frac{1}{2}$. Can you hande from here?