1. Let X be a draw from a box containing 2 tickets with the number (-1) and one ticket with the

number (+1). Find the entropy of X in bits. Choose the closest.

(A) 0.92

(B) 0.5

(C) 0.75

(D) 2

(E) 1

2. Toss a fair coin until you get heads for the first time. Find the entropy (in bits) of the number

of tosses required. Choose the closest.

(A) 0.5

(B) 0.75

(C) 1

(D) 1.5

(E) 2

3. Let I(A) denote the information separation (Kullback number) in nats (log base e), between

a Poisson with parameter X>0 and a Poisson with parameter > 0. Which of the following

propositions are correct?

1. I(1:2) 1 - log 2

=

2. I(1:3) = 2log 3.

2

3. I(2:3) = 1 + 2log 5