PHY3703 ASSIGNMENT 2 FULL SOLUTIONS COMPLETE SOLUTIONS MEMORANDUM UNISA 2026 STATISTICAL AND THERMAL PHYSICS

PHY3703
ASSIGNMENT 2
FULL SOLUTIONS
COMPLETE SOLUTIONS

MEMORANDUM
UNISA
2026
Page 1 of 18

,SOLUTION:

(a) Fair Coin
1 1
Probability distribution: 𝑝1 = 2 , 𝑝2 = 2
2

𝑆 = − ∑ 𝑝𝑖 log⁡2 𝑝𝑖
𝑖=1


Page 2 of 18

, 𝑆 = −(𝑝1 log⁡2 𝑝1+𝑝2 log⁡2 𝑝2 )
1 1 1 1
𝑆 = − (2 log⁡2 2 + 2 log⁡2 2)


1
Since log⁡2 2 = log⁡2 2−1 = −1:

1 1
𝑆 = − ( × (−1) + × (−1))
2 2
1 1
𝑆 = − ( − 2 − 2)
𝑆 = −(−1) = 1
𝑆 = 1 bit




(b) Biased Coin
1 4
Probability distribution: 𝑝1 = 5 , 𝑝2 = 5
2

𝑆 = − ∑ 𝑝𝑖 log⁡2 𝑝𝑖
𝑖=1
𝑆 = −(𝑝1 log⁡2 𝑝1+𝑝2 log⁡2 𝑝2 )
1 1 4 4
𝑆 = − ( log⁡2 + log⁡2 )
5 5 5 5

1
Compute log⁡2 5:

1
log⁡2 = log⁡2 5−1 = −log⁡2 5
5
ln 5 1.609437912
log⁡2 5 = ≈ ≈ 2.321928095
ln 2 0.693147181


Thus:
1
log⁡2 ≈ −2.321928095
5

4
Compute log⁡2 5:



Page 3 of 18