Читать книгу Probability and Statistical Inference - Robert Bartoszynski - Страница 4

1 Chapter 1Figure 1.1 Possible seatings of persons A and B at a square table.Figure 1.2 Possible seatings of any two persons at a square table.Figure 1.3 Possible seatings of one person if the place of the other person ...Figure 1.4 Scheme of a randomized response.Figure 1.5 Complement, union, and intersection.Figure 1.6 The first De Morgan's law.Figure 1.7 Complement of a Rectangle.

2 Chapter 2Figure 2.1 Hitting a target.Figure 2.2 First solution of Bertrand's problem.Figure 2.3 Second solution of Bertrand's problem.Figure 2.4 Third solution of Bertrand's problem.Figure 2.5 Explanation of Bertrand's paradox.Figure 2.6 Union of two events.Figure 2.7 Union of three events.

3 Chapter 3Figure 3.1 Pascal's triangle.Figure 3.2 Process of counting votes.Figure 3.3 Reflection principle.

4 Chapter 4Figure 4.1 Possible results of the two first draws in Example 4.5.Figure 4.2 Transitions in model of epidemic.

5 Chapter 5Figure 5.1 Cdf of the distance from the center of the target.Figure 5.2 Cdf of the number of heads in three tosses of a coin.Figure 5.3 Cdf of random variable X.Figure 5.4 Cdf of distribution uniform on .

6 Chapter 6Figure 6.1 Shadows and sections of domain of integration.Figure 6.2 Support of density and the set .Figure 6.3 A function that is not a cdf but satisfies (a)–(d).Figure 6.4 Marginal density.Figure 6.5 Condition for dependence.Figure 6.6 Probability of better of two attempts exceeding 0.75.Figure 6.7 Three‐component system.Figure 6.8 Joint distribution of and .Figure 6.9 Options for marginal densities of and .Figure 6.10 Conditional densities.Figure 6.11 Triangular density.Figure 6.12 Supports of and .Figure 6.13 Approximations of two conditioning events.Figure 6.14 First two generations in the process of grinding.

7 Chapter 7Figure 7.1 Interpretation of expected value of a discrete random variable.Figure 7.2 Interpretation of expected value of a continuous random variable....Figure 7.3 Approximating sums for Riemann and Lebesgue integrals.Figure 7.4 Graph of and its cdf.Figure 7.5 Nonintegrable function whose iterated integrals exist and are not...Figure 7.6 Nonintegrable function whose iterated integrals exist and are equ...Figure 7.7 Length of 16 feet (Drawing by S. Niewiadomski).Figure 7.8 Two weightings of A and B.Figure 7.9 Dependent but uncorrelated random variables.

8 Chapter 8Figure 8.1 Flowchart.Figure 8.2 Series system.Figure 8.3 Parallel system.Figure 8.4 Series‐parallel system.Figure 8.5 Flowchart.Figure 8.6 Two regression lines.Figure 8.7 Shapes of beta distributions.

9 Chapter 10Figure 10.1 Lifetime T(t*) of a bulb.

10 Chapter 11Figure 11.1 Likelihood function for the range in uniform distribution.Figure 11.2 Likelihood function for five Bernoulli trials.

11 Chapter 12Figure 12.1 Power functions and .Figure 12.2 Power functions of tests and .Figure 12.3 Power of the two‐sided test .Figure 12.4 Partition into sets .Figure 12.5 Power functions of a one‐sided UMP test (dashed line) and a UMPU...Figure 12.6 Power function of an unbiased test.Figure 12.7 Golden rectangles.

12 Chapter 13Figure 13.1 True regression.Figure 13.2 Linear regression for uniform distribution of .Figure 13.3 Ages of Polish kings and their heirs at death.Figure 13.4 (a) No effects of or . (b) No effect of , effect of , no in...

13 Chapter 16Figure 16.1 Posterior densities (dashed line) for different prior densities ...Figure 16.2 The 90% central credible interval (dotted line) and the 90% high...

14 1Figure A.1 The densities of BETA(2, 5), BETA(3, 3), and BETA(1, 4) distribut...Figure A.2 Histogram of the data generated from the BETA(2, 3) distribution ...Figure A.3 Histogram of the data generated from the BETA(2, 3) distribution ...