1. Further distributions

2. Discrete random variables

3. Expectation and variance
Read Examples , pp
Do Q1-Q7, p.261

4. Linear combinations of normal variables
Read Examples , pp
Do Q1-Q4, p.417

5. The Poisson distribution

6. Properties of the Poisson distribution
Read Examples , pp
Do Q1-Q10, pp

7. The sum of independent Poisson variables
Read Examples 5.25 & 5.26, pp
Do Exercise 5f, p.303

8. Continuous random variables
Read Examples 6.1 – 6.4, pp
Do Exercise 6a, pp

9. Expectation Read Examples 6.5 – 6.7, pp.320-323
Do Exercise 6b, pp
Read Examples 6.8 – 6.10, pp

10. Variance and mode Read Examples 6.11 – 6.15, pp.328-333
Do Exercise 6c, pp

11. Cumulative distribution function

12. Median, quartiles and other percentiles
Read Examples 6.16 & 6.17, pp
Do Exercise 6d, pp

13. Cumulative distribution function
Read Examples , pp
Cumulative distribution function
Do Exercise 6e, pp

14. Uniform distribution Read Examples 6.21 - 6.26, pp.345-349
Do Exercise 6f, pp

15. The p.d.f. of a related variable
Frequently, the random variable being measured is not the ultimate objective. What many be of primary interest is some function of these variables.
p.d.f. of X
c.d.f. of X
c.d.f. of Y
p.d.f. of Y

16. Example 1

17. Example 2

18. Questions

19. The geometric distribution
Read Examples 5.2, pp
The geometric distribution

20. The geometric distribution
Read Examples , pp
Do Exercise 5a, pp

21. Deriving the (negative) exponential distribution
Differentiating yields:

22. The exponential distribution
and so:

23. Example 1

24. Shape of the exponential distribution

25. Expectation and variance of the exponential distribution

26. Example 1

27. Example 2

28. Questions 1. 2. 3. 4. 5. 6.