l distribution as a model Flashcards","topicId":"21ae3385-e68e-4542-88b0-9f274e16bc3b","topicSlug":"binomial-distribution-as-a-model","cards":[{"id":"99238765-7d3a-479e-98c4-a6d5aac64b55","cardType":"cloze","front":"A Bernoulli trial has exactly [ ] possible outcomes.","back":"A Bernoulli trial has exactly two possible outcomes.","points":null,"mcqOptions":null},{"id":"a618d33d-b06c-4922-9153-4440b4aabbbc","cardType":"basic","front":"If success has probability $p$, what is the failure probability?","back":"The failure probability is $1-p$.","points":1,"mcqOptions":null},{"id":"968b4b01-f7db-4fae-b0d7-26e74cf632c0","cardType":"basic","front":"Must a binomial “success” be a desirable outcome?","back":"No - success is simply the outcome being counted.","points":1,"mcqOptions":null},{"id":"435397cd-e682-4c9f-aea7-e67ae41a75ae","cardType":"basic","front":"What does the random variable $X$ count in a binomial model?","back":"$$X$ counts the number of successes.","points":1,"mcqOptions":null},{"id":"24d31fac-1dbf-4e85-914d-8f5c64602f7f","cardType":"basic","front":"Which four BINS conditions are required for a binomial model?","back":"

Binary outcomes
Independent trials
Fixed number of trials
Constant probability of success

","points":3,"mcqOptions":null},{"id":"fda4482e-2ab7-491b-a99f-f9107e5c35a8","cardType":"cloze","front":"The notation $\\text{[...]}$ means that $X$ has a binomial distribution with $n$ trials and success probability $p$.","back":"The notation $\\boxed{X\\sim B(n,p)}$ means that $X$ has a binomial distribution with $n$ trials and success probability $p$.","points":null,"mcqOptions":null},{"id":"fe006b48-e63f-47a2-b2be-8b07e290f40a","cardType":"basic","front":"What values can $X\\sim B(n,p)$ take?","back":"$X=0,1,2,\\ldots,n$.","points":1,"mcqOptions":null},{"id":"921f0084-e5d0-4588-9bb6-b900881c0f63","cardType":"cloze","front":"A binomial random variable is [ ], so it cannot take values such as 2.5 successes.","back":"A binomial random variable is discrete, so it cannot take values such as 2.5 successes.","points":null,"mcqOptions":null},{"id":"82f9faf1-20c5-40a0-8e1d-0af4ec972a2c","cardType":"basic","front":"Why can sampling without replacement make a binomial model unsuitable?","back":"The changing population composition makes trials dependent.","points":2,"mcqOptions":null},{"id":"0201b2b3-e837-4acf-8ab0-f0306698a5ee","cardType":"basic","front":"When may a binomial model approximate sampling without replacement?","back":"When the population is much larger than the sample.","points":1,"mcqOptions":null},{"id":"8173417c-4414-45cd-852b-7b4c112d6b9b","cardType":"cloze","front":"For $X\\sim B(n,p)$, $\\text{[...]}$.","back":"For $X\\sim B(n,p)$, $\\boxed{P(X=r)=\\binom{n}{r}p^r(1-p)^{n-r}}$.","points":null,"mcqOptions":null},{"id":"491d8504-46d8-48bd-949b-48efe1203e33","cardType":"basic","front":"What does $\\binom{n}{r}$ count in the binomial probability formula?","back":"The arrangements of the $r$ successes.","points":1,"mcqOptions":null},{"id":"8669fcb2-91e0-4eb3-ac52-9c7828a2a941","cardType":"basic","front":"What does $p^r$ represent in the binomial probability formula?","back":"The probability contribution from the $r$ successes.","points":1,"mcqOptions":null},{"id":"de6692af-a244-4ade-9cf4-549aadbbb7f6","cardType":"basic","front":"What does $(1-p)^{n-r}$ represent in the binomial probability formula?","back":"The probability contribution from the $n-r$ failures.","points":1,"mcqOptions":null},{"

2.4.2 Binomial distribution as a model Flashcards

2.4.2 Binomial distribution as a model Flashcards