Years with annual maxima river discharge equaling or exceeding 60 000 m3/s for River Brahmaputra near Bahadurabad, near India-Bangladesh Border (1987-1995) and corresponding recurrence intervals are listed in Table 1. Estimate the probability that the annual maxima discharge will exceed 60 000 m3/s at least once during the next three years?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Years with annual
Table 1
| Exceedance year | 1987 | 1988 | 1989 | 1990 | 1991 | 1992 | 1993 | 1994 |
| Recurrence Interval (years) | 4 | 1 | 1 | 16 | 3 | 6 | 5 | 5 |
To calculate the probability that there would be at least one annual maxima discharge exceeding 60,000:
Given data:
| Exceedance year | Recurrence Interval (years) |
| 1987 | 4 |
| 1988 | 1 |
| 1989 | 1 |
| 1990 | 16 |
| 1991 | 3 |
| 1992 | 6 |
| 1993 | 5 |
| 1994 | 5 |
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