Matematik

Discrete Uniform

28. november 2016 af Rossa - Niveau: Universitet/Videregående

Hej derude.
Vil nogen derude hjælpe med at forstå en eksampel fra bogen.

Example 3.5.2
There are 100 slips of paper in a hat, each of which has one of the numbers 1,2,…..,1000 written on it , with no number appearing more than once. Five of the slips are drawn, one at a time.
(First consider random sampling with replacement (with equal probabilities)).

a) What is the distribution of how many of the drawn slips have a value a value of at least 80 written on them?

Solution:
a) By the story of the binomial, the distribution is Bin(5,0.21)

Jeg kan se, at n=5, og jeg forstår, at p =0.21, og hvis det er rigtigt, hvordan kan p være lig med 0.21?

På forhånd tak

Brugbart svar (0)

Svar #1
28. november 2016 af Soeffi

#0 There are 100 slips of paper in a hat, each of which has one of the numbers 1,2,…,100

Svar #2
28. november 2016 af Rossa

Det skal være "1,2,.....,100".

Bogen findes her: https://books.google.dk/books?id=EvoYCwAAQBAJ&pg=PA106&lpg=PA106&dq=example+3.5.2(Random+slips+of+paper)&source=bl&ots=AyTiQORFjN&sig=1QBXhtNSi77cKdF0RwBMnRGBNB0&hl=da&sa=X&ved=0ahUKEwiRqZ6yzMvQAhXKO5oKHTUMCpoQ6AEIHDAA#v=onepage&q=example%203.5.2(Random%20slips%20of%20paper)&f=false

Brugbart svar (1)

Svar #3
29. november 2016 af Therk

p = 0.21 fordi

$\sum_{i = 1}^{100} 1_{\{i\geq 80\}} =21$

(fra og med 80 og til og med 100 er der 21 tal)

Det er en binomialfordeling, fordi det er sampling med replacement (5 uafhængige bernoulliforsøg).

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