4. Xi = 1 if ith access is a hit, 0 if miss.
1st miss on kth access
1st access=hit
k-1 access=hit
kth access miss

6. Marginal pmfs

7. Derivation of (2.8) and (2.9)

11. Solution...

12. 2.4 Expectation

13. 2.4 Expectation

14. Example 2.22 (Poisson RV)

16. Special Care is Required Sometimes

18. If Y = g(X); i.e., Y(ω) = g(X(ω)), to compute E[Y]
requires the pmf of Y, or does it...

19. Law of the Unconscious Statistician (LOTUS)
And
Leads to linearity and other properties...

20. Moments nth moment: E[X n], n = 1, 2, 3, . . .
nth central moment: E[(X-m)n], m := E[X]
Variance = 2nd central moment
σ 2 := var(X) := E[(X-m)2]

21. Variance formula:
Derivation:

22. Example 2.29 (Poisson RV)

23. Indicator Functions

25. The Markov Inequality For X ≥ 0 and a > 0, follows from
Derivation . . .

26. The Chebyshev Inequality

27. The Chebyshev Inequality
To derive this, take X = |Y| and r = 2 in (2.19):