7 Suppose (5, n) assumes only the possible pairs (-1,0), (1,1), (-1,2), (3,2), (4,1) with probabilities 1/6, 1/3, 1/12, 1/6, 1/4 respectively, list the probability distribution table of (, n) and write out the marginal distribution of &.
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!
7. Given: The data is as follows:
| possible pairs of () | Probability |
| (-1,0) | |
| (1,1) | |
| (-1,2) | |
| (3,2) | |
| (4,1) |
The probability distribution of table of () is:
| () | 0 | 1 | 2 | Row total |
| -1 | 0 | |||
| 1 | 0 | 0 | ||
| 3 | 0 | 0 | ||
| 4 | 0 | 0 | ||
| Column Total | 1 |
Note: Since, the probabilities are not mentioned for few of the pairs of (). Therefore, the probability for those pairs will be 0.
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