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Statistics Unit 6
| Term | Definition |
|---|---|
| probability distribution | values add up to 100%, shows possible outcomes and their probabilities |
| mean/expected value of probability distributions | outcome value (ex. 1, 2, 5, 100) times the probability of that outcome happening (do this for all sets of outcomes and probabilities or use menu 611 in calc) |
| standard deviation of probability distributions | use menu 611 or √(Xi - mean)(Pi) |
| interpreting expected value/mean (probability dist) | The average number of (context) in the long run of randomly choosing many many (context) is (mean) |
| interpreting standard deviation (probability dist) | The (context) typically variesby (standard deviation) from the mean of (mean) |
| expected value can be... | positive or negative (ex. when someone loses money) |
| discrete random variable | countable, has gaps, no decimals (ex. people) |
| continuous random variable | measure able, has no gaps, infinite # of outcomes, decimals (ex. money, height, weight) |
| continuous random variables can be... | normal (use NormCdf) or uniform (c-b/c-a) |
| combining means with addition | μ (x+y) = μx + μy |
| combining means with subtraction | μ (x+y) = μx - μy |
| combining standard deviations with addition or subtraction | σ (x+ y or x-y) = √σx²+σy², save multiplication transformation for last |
| variance | standard deviation squared, factor in all probabilities and can be added when combined (similar to means) |
| transforming with additon/subtraction | shape - same, center - add/subtract by the value, center - same |
| transforming with multiplication/division | shape - same, center - multiply/divide by the value, center - multiply/divide by the value |
| conditions for binomial random variables | B - binary outcomes, define success/failure I - independence N - fixed number of trials S - constant probability of success |
| formula for probability of binomial random variables | (nCx) * (p)^x * (1-p)^(n-x), n = # of trials, x = # of successes, p = probability of success, 1-p = probability of failure (can also use binomCdf/Pdf) |
| when to use binom/genomPdf | when question is asking for a set number of successes (n, p, x) |
| when to use binom/Cdf | when question is asking for ≤, ≥, <, > a number of successes (n, p, min, max), no infinity, when given > or < use the second lowest/highest number (ex. p < 2 type in upper bound as 1) |
| mean of binomial random variables | μ = n × p |
| standard deviation of binomial random variables | √p(n)(1-p) |
| 10% condition | if sampling without replacement (events aren't independent), independence can be assumed if sample size is less than 10% of the population, n ≤ 0.1(N) |
| large counts condition | used to check if binomial random variable is normal, if n x p ≥ 10 and n(1-p) ≥ 10 |
| conditions for geometric random variables | B - binary outcomes I - independence (normally right skewed) F - first success S - set probability |
| formula for probability of geometric random variables | P(x=k) = (1-p^)k-1 x (p) |
| mean of geometric random variables | μ= 1/p |
| standard deviation of geometric random variables | σ=√1-p/p |
| when to use genomCdf | when question is asking for ≤, ≥, <, > a number of successes (n, p, min, max), can use infinity, use numbers given in question |
| transforming variance | multiply/divide by the value^2 (not just the value), only affected by multiplication/division |
| finding height of uniform distribution | 1/b-a (the interval) |
| finding probability with a uniform distribution | d-c (c < x < d) x height |
| in order to combine means/standard deviations... | the variables must be independent |
Created by:
ts2819