43)

E(X)=(3*1+2*5+4*6+1*7)/10=4.4 .

P(0)=1*1/2^3 = 0.125

P(1) =3*1/2^3 = 0.375

P(2) =3*1/2^3 = 0. 375

P(3) =1*1/2^3 = 0.125

Then, the mean number of heads will be:

E(X)=P(0)*0+ P(1)*1+ P(2)*2+ P(3)*3=

=0.125*0+0.375*1+0.375*2+0.125*3=1.5

QUESTION: Do you understand why 1.5 is the logical answer?

P(0)=1*1/2^4 = 0.0625

P(1) =4*1/2^4 = 0.25

P(2) =6*1/2^4 = 0. 375

P(3) =4*1/2^4 = 0.25

P(4) =1*1/2^4 = 0.0625

Now, the mean number of heads is equal to:

E(X)=P(0)*0+ P(1)*1+ P(2)*2+ P(3)*3+ P(4)*4=

=0.0625*0+0.25*1+0.375*2+0.25*3+0.0625*4=2

QUESTION: Do you understand why 2 is the logical answer?