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Engineering Probability Class 17 Thu 2022-03-17

Source

1 Chapter 5, Two Random Variables, 3

  1. Example 5.9, page 242.

  2. Example 5.16, page 252.

  3. Example 5.17, page 253.

2 Sect 5.5 Independence, page 254

  1. Example 5.19 on page 255.

  2. Example 5.20, page 255.

  3. Independence: Example 5.22 on page 256. Are 2 normal r.v. independent for different values of $\rho$ ?

3 Sect 5.6 Joint moments, p 257

  1. Example 5.24, sum.

  2. Example 5.25, product.

  3. Example 5.26 page 259. Covariance of independent variables.

  4. Correlation coefficient.

  5. Example 5.27 page 260 uncorrelated but dependent. Correlation measures linear dependence. If the dependence is more complicated, the variables may be dependent but not correlated.

4 Sect 5.7 Conditional page 261

  1. Example 5.29 loaded dice

  2. 5.6.2 Joint moments etc

    1. Work out for 2 3-sided dice.

    2. Work out for tossing dart onto triangular board.

  3. Example 5.30.

  4. Covariance, correlation coefficient.