nhị thức, hoặc phân phối nhị thức tiêu cực, một phiên bản của các định lý giới hạn trung tâm chỉ ra rằng, như A, m, T, tương ứng, đi đến vô cùng, phân phối của S trở nên bình thường. Trong ví dụ này, E (N) nhỏ để phân phối của S là có khả năng bị sai lệch. | DISTRIBUTION FUNCTIONS AND RELATED CONCEPTS 29 Fig. Hazard rate function for Model 1 s c 0 0 500 1 000 1 500 2 000 2 500 3 000 X Fig. Hazard rate function for Model 2 calculations. In this book such values will be arbitrarily defined so that the function is right A variety of commonly used continuous distributions are presented in Chapter 4 and many discrete distributions are presented in Chapter 5. An interesting characteristic of a random variable is the value that is most likely to occur. 4By arbitrarily defining the value of the density or hazard rate function at such a point it is clear that using either of them to obtain the survival function will work. If there is discrete probability at this point in which case these functions are left undefined then the density and hazard functions are not sufficient to completely describe the probability distribution. 30 BASIC PROBABILITY CONCEPTS Definition The mode of a random variable or equivalently of a distribution is the most likely value of the random variable. For a discrete variable it is the value with the largest probability. For a continuous variable it is the value for which the density function is largest. Example Determine the mode for Models 1-5. Model 1 The density function is constant. All values from 0 to 100 could be the mode or equivalently it could be said that there is no single mode. Model 2 The density function is strictly decreasing and so the mode is at 0. Model 3 The probability is largest at 0 so the mode is at 0. Model 4 As a mixed distribution it is not possible to define a mode for Model 4. Model 5 The density function is constant over two intervals with higher values from 50 to 75. The values between 50 and 75 are all modes or equivalently it could be said that there is no single mode. MOMENTS The moments of a distribution are characteristics that can be used in describing a .
