1. Correct. The answer is false

 

You should calculate the expected return using the definition of discrete expectation. In this particular case:

 

E(Z) = ∑ z(1/2)z

z=1

E(Z) = 1/2 + 2(1/4) + 3 (1/8) + . . .

 

This is an infinite sum of values less than 1. Hence, the sum converges to a finite value. To find this sum, let

 

S = 1/2 +2(1/4) + 3(1/8) + 4(1/16) + . . .

 

Then,

(1/2)S = (1/4) +2(1/8) +3(1/16) + . .

 

Subtracting (1/2)S from S,

 

(1/2)Q = 1/2+ (1/4) + (1/8) + (1/16)+ . . =1.

 

Thus

E(Z)= S = 2 ($ ten thousands).