Dear BlakeRobertsonMD,

definition:

E = p1*v1 + p2*v2 + ... + pn*vn, where

n means the amount of events,

p2 means the probality of the second event,

v2 means the value of the second event.

Now n = 4, because "the number of heads" can be 0, 1, 2 or 3.

So v1=0, v2=1, v3=2, v4=3.

p1 = p(nothing heads) = 1/8.

p4 = p(all heads) = 1/8.

p2 = p(exactly one head) = p(the first head others tails) + p(the second head others tails) + p(the 3th head others tails) = 1/8 + 1/8 + 1/8 = 3/8.

I leave for you p3 and E.