So­lu­tion esda-a


Sup­pose you toss a coin a large num­ber of times, and count heads as one, tails as two. What will be the ex­pec­ta­tion value?


For a fair coin, the prob­a­bil­ity of heads or tails is the same; each will have a prob­a­bil­ity of 50% or $\frac 12$. So the ex­pec­ta­tion value is $\frac 12\times 1+\frac 12\times 2$ $\vphantom0\raisebox{1.5pt}{$=$}$ 1.5. This will be the av­er­age value you ob­tain in a large num­ber of throws.