Further distributions

Discrete random variables

Expectation and variance Read Examples 4.18-4.20, pp.257-260 Do Q1-Q7, p.261

Linear combinations of normal variables Read Examples 8.1-8.11, pp.403-417 Do Q1-Q4, p.417

The Poisson distribution

Properties of the Poisson distribution Read Examples 5.18-5.21, pp.292-295 Do Q1-Q10, pp.297-298

The sum of independent Poisson variables Read Examples 5.25 & 5.26, pp.301-302 Do Exercise 5f, p.303

Continuous random variables Read Examples 6.1 – 6.4, pp.315-319 Do Exercise 6a, pp.319-320

Expectation Read Examples 6.5 – 6.7, pp.320-323 Do Exercise 6b, pp.323-324 Read Examples 6.8 – 6.10, pp.325-327

Variance and mode Read Examples 6.11 – 6.15, pp.328-333 Do Exercise 6c, pp.333-334

Cumulative distribution function

Median, quartiles and other percentiles Read Examples 6.16 & 6.17, pp.336-339 Do Exercise 6d, pp.339-341

Cumulative distribution function Read Examples 6.18 - 6.20, pp.341-343 Cumulative distribution function Do Exercise 6e, pp.343-344

Uniform distribution Read Examples 6.21 - 6.26, pp.345-349 Do Exercise 6f, pp.349-350

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

Example 1

Example 2

Questions

The geometric distribution Read Examples 5.2, pp.273 - 274 The geometric distribution

The geometric distribution Read Examples 5.3 -5.6, pp.274 - 276 Do Exercise 5a, pp.276 - 277

Deriving the (negative) exponential distribution Differentiating yields:

The exponential distribution and so:

Example 1

Shape of the exponential distribution

Expectation and variance of the exponential distribution

Example 1

Example 2

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