ผลต่างระหว่างรุ่นของ "Probstat/week4 practice 1"
Jittat (คุย | มีส่วนร่วม) |
Jittat (คุย | มีส่วนร่วม) |
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| แถว 4: | แถว 4: | ||
=== Random hats === | === Random hats === | ||
A group of '''n''' people, each wearing a different hat, go to the museum. They have to leave their hats at the entrance. When they get back, each gets a random hat back. We are interested in the number of people who get their own hat back. | A group of '''n''' people, each wearing a different hat, go to the museum. They have to leave their hats at the entrance. When they get back, each gets a random hat back. We are interested in the number of people who get their own hat back. | ||
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| + | Let random variable '''X''' be the number of people who get their own hat back. As a typical way of using linearity of expectation, we shall define an indicator random variable '''X<sub>i</sub>''' to be 1 if person '''i''' gets her/his hat back, and 0, otherwise. | ||
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| + | 1. What is '''E[X<sub>i</sub>]'''? | ||
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| + | 2. What is '''E[X]'''? (Show your work.) | ||
=== Dinner on a circle table === | === Dinner on a circle table === | ||
| + | The same group of '''n''' people go into a Chinese restaurant. They sit on a circular table with a circular turntable (see [http://en.wikipedia.org/wiki/Lazy_Susan wikipedia article]). Each person orders one different dish and gets her/his order exactly in front of her/him. To make a fun dinner, they decide to randomly rotate the turntable so that each one of them will hopefully get a random dish. | ||
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| + | Let random variable '''Y''' be the number of people who get their own dish after the random rotation. | ||
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| + | 1. What is '''E[Y]'''? (In this case, you probably don't need to use the linearity of expectation.) | ||
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| + | === Expectation and probability === | ||
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== Binomial random variable == | == Binomial random variable == | ||
รุ่นแก้ไขเมื่อ 01:22, 9 กันยายน 2557
เนื้อหา
Two experiments
In this section, we shall analyze two experiments.
Random hats
A group of n people, each wearing a different hat, go to the museum. They have to leave their hats at the entrance. When they get back, each gets a random hat back. We are interested in the number of people who get their own hat back.
Let random variable X be the number of people who get their own hat back. As a typical way of using linearity of expectation, we shall define an indicator random variable Xi to be 1 if person i gets her/his hat back, and 0, otherwise.
1. What is E[Xi]?
2. What is E[X]? (Show your work.)
Dinner on a circle table
The same group of n people go into a Chinese restaurant. They sit on a circular table with a circular turntable (see wikipedia article). Each person orders one different dish and gets her/his order exactly in front of her/him. To make a fun dinner, they decide to randomly rotate the turntable so that each one of them will hopefully get a random dish.
Let random variable Y be the number of people who get their own dish after the random rotation.
1. What is E[Y]? (In this case, you probably don't need to use the linearity of expectation.)
