ผลต่างระหว่างรุ่นของ "Probstat/notes/random variables"
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Jittat (คุย | มีส่วนร่วม) |
Jittat (คุย | มีส่วนร่วม) |
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| แถว 3: | แถว 3: | ||
In many cases, after we perform a random experiment, we are interested in certain quantity from the outcome, not the actual outcome. In that case, we can define a ''random variable'', which is a function from the sample space to real numbers, to represent the random quantity that we are interested in. | In many cases, after we perform a random experiment, we are interested in certain quantity from the outcome, not the actual outcome. In that case, we can define a ''random variable'', which is a function from the sample space to real numbers, to represent the random quantity that we are interested in. | ||
| − | For example, consider the following experiment. We toss two dice. Let a random variable ''X'' be the sum of the values of these two dice. | + | For example, consider the following experiment. We toss two dice. Let a random variable ''X'' be the sum of the values of these two dice. The table below shows the outcomes and probabilities related to ''X''. |
| + | |||
| + | {| class="wikitable" | ||
| + | | ''i'' | ||
| + | | Outcomes for which ''X'' = ''i'' | ||
| + | | Probability ''P{ X = i }'' | ||
| + | |- | ||
| + | |2 | ||
| + | | (1,1) | ||
| + | | 1/36 | ||
| + | |- | ||
| + | |3 | ||
| + | | (1,2), (2,1) | ||
| + | | 2/36 | ||
| + | |- | ||
| + | |4 | ||
| + | | (1,3), (2,2), (3,1) | ||
| + | | 3/36 | ||
| + | |- | ||
| + | |5 | ||
| + | | (1,4), (2,3), (3,2), (4,1) | ||
| + | | 4/36 | ||
| + | |- | ||
| + | |6 | ||
| + | | (1,5), (2,4), (3,3), (4,2), (5,1) | ||
| + | | 5/36 | ||
| + | |- | ||
| + | |7 | ||
| + | | (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) | ||
| + | | 6/36 | ||
| + | |- | ||
| + | |8 | ||
| + | | (2,6), (3,5), (4,4), (5,3), (6,2) | ||
| + | | 5/36 | ||
| + | |- | ||
| + | |9 | ||
| + | | (3,6), (4,5), (5,4), (6,4) | ||
| + | | 4/36 | ||
| + | |- | ||
| + | |10 | ||
| + | | (4,6), (5,5), (6,4) | ||
| + | | 3/36 | ||
| + | |- | ||
| + | |11 | ||
| + | | (5,6), (6,5) | ||
| + | | 2/36 | ||
| + | |- | ||
| + | |12 | ||
| + | | (6,6) | ||
| + | | 1/36 | ||
| + | |} | ||
A random variable ''X'' also induces events related to it. For example, we can consider the event that ''X=10''. | A random variable ''X'' also induces events related to it. For example, we can consider the event that ''X=10''. | ||
รุ่นแก้ไขเมื่อ 02:33, 18 กันยายน 2557
- This is part of probstat.
In many cases, after we perform a random experiment, we are interested in certain quantity from the outcome, not the actual outcome. In that case, we can define a random variable, which is a function from the sample space to real numbers, to represent the random quantity that we are interested in.
For example, consider the following experiment. We toss two dice. Let a random variable X be the sum of the values of these two dice. The table below shows the outcomes and probabilities related to X.
| i | Outcomes for which X = i | Probability P{ X = i } |
| 2 | (1,1) | 1/36 |
| 3 | (1,2), (2,1) | 2/36 |
| 4 | (1,3), (2,2), (3,1) | 3/36 |
| 5 | (1,4), (2,3), (3,2), (4,1) | 4/36 |
| 6 | (1,5), (2,4), (3,3), (4,2), (5,1) | 5/36 |
| 7 | (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) | 6/36 |
| 8 | (2,6), (3,5), (4,4), (5,3), (6,2) | 5/36 |
| 9 | (3,6), (4,5), (5,4), (6,4) | 4/36 |
| 10 | (4,6), (5,5), (6,4) | 3/36 |
| 11 | (5,6), (6,5) | 2/36 |
| 12 | (6,6) | 1/36 |
A random variable X also induces events related to it. For example, we can consider the event that X=10.
