maths.free › Statistics & Probability › Counting: permutations and combinations
Counting: permutations and combinations
Factorials, ordered and unordered selections.
n! counts the orderings of n things. Choosing k of them in order is n!/(n − k)!; ignoring the order divides by k! again, giving the binomial coefficient “n choose k”. These numbers are Pascal's triangle and the coefficients of (a + b)ⁿ.
ឧទាហរណ៍ដែលបានធ្វើ · 5 choose 2
ជំហានដោយជំហាន
- \binom{5}{2} = \frac{5!}{2!\,(5-2)!}
Unordered selections: n! / (k! (n−k)!).
- = \frac{120}{2 \times 6} = 10
បង្ហាញចម្លើយ
ឥឡូវអ្នក ជ្រើសបញ្ហា ឬវាយបញ្ចូល ឬគូររបស់អ្នកផ្ទាល់ ។ ជំហាននីមួយៗ រូបភាព ចម្លើយត្រូវបានលាក់រហូតដល់អ្នកសួរ ។
គណនីឥតគិតថ្លៃបន្ថែមចំណាំលើមេរៀននីមួយៗ កំណត់ហេតុនៃអ្វីដែលអ្នកបានបញ្ចប់ បញ្ហាដែលអ្នកបានដោះស្រាយនៅកន្លែងមួយ និងគ្រូដែលអ្នកអាចសួរអំពីទំព័រនេះ ។ គណិតវិទ្យាដោយខ្លួនវាគឺបើកចំហសម្រាប់អ្នកទាំងអស់គ្នា ចុះឈ្មោះចូល ឬមិនចុះឈ្មោះចូល ។
ចុះឈ្មោះ ចូលនិមិត្តសញ្ញាដែលបានប្រើនៅទីនេះ
ចុចនិមិត្តសញ្ញាណាមួយសម្រាប់ការកំណត់ពេញលេញ រូបភាព និងតួអក្សរនីមួយៗមានន័យអ្វី ។
របៀប: Counting: permutations and combinations
- Unordered selections: n! / (k! (n−k)!).
សំណួរដែលមនុស្សសួរ
Mean or median, which should I use?
Median when the data have outliers or a long tail (incomes, house prices); mean when the data are roughly symmetric and you want every value to count. Report both if they disagree. The gap is itself information.
What does a p-value actually say?
The probability of seeing data at least this extreme if the null hypothesis were true. It is not the probability that the null hypothesis is true.
Why divide by n − 1 for the sample variance?
The sample mean sits closer to the sample than the true mean does, so squared deviations from it are slightly too small on average; dividing by n − 1 instead of n corrects the bias.
បន្ថែមទៀតក្នុង Statistics & Probability
Sampling and dataDescribing data with graphsMean, median and modeProbabilityDiscrete random variablesContinuous random variablesThe normal distributionThe central limit theoremConfidence intervalsHypothesis testingComparing two samplesChi-square testsLinear regression and correlationANOVA and the F distribution