zadania z prawdopodobienstwa

Jataman
Użytkownik
Użytkownik
Posty: 4
Rejestracja: 17 sie 2014, o 16:16
Płeć: Mężczyzna
Lokalizacja: Kraków

zadania z prawdopodobienstwa

Post autor: Jataman » 25 kwie 2021, o 16:12

Szukam korepetytora do odpłatnego rozwiązania i wytłumaczenia mi poniższych zadań.

Mary is exploring a very simple language in which strings are formed by sequentially drawing
each token from the vocabulary V independently and uniformly at random. Mary wants
to construct a corpus in this language. She does so by sampling x1, x2, x3, . . . from her
vocabulary until the corpus is the size she wants.

(a) Mary draws n tokens to form her corpus.
(i) What is the expected number of distinct tokens that appear?
(ii) What is the probability that all |V | of the words from the vocabulary have ap-
peared?

(b) Mary wants the bigram work hard to appear in the corpus.
(i) What is the expected number of tokens that will be drawn from the vocabulary
before this bigram appears?
(ii) Mary decided that this number is quite big. Instead, she would at least like to
ensure that the word work appears in the text with probability ≥ 95%. What is
the number of tokens she needs to draw before this happens?

(c) One thing Mary dislikes is when the same words appear next to each other in her
corpus.
(i) What is the expected number of draws before two of the same tokens appear next
to each other?
Rekrutacja Instytut Matematyczny, Uniwersytet Wrocławski (gif)

ODPOWIEDZ