Statistik 1

Typvärdet

"mode"

Mutually Exhaustive Variales

exhaustive variables are variables that represent distinct categories or events, and no outcome can belong to more than one category simultaneously. In other words, the categories represented by mutually exhaustive variables do not overlap

Intervallskala

has equal intervals between values, but it lacks a true zero point. Temperature measured in Celsius or Fahrenheit is a common example. Differences between values are meaningful, but ratios are not. = when both order and equal differences matter but ratios don't

Sharpe-kvot visar

hur väl avkastningen kompenserar för risk - Ju större Sharpe-kvot, desto bättre kompenserartillgången investeraren för risk

When are P-values used

in hypothesis testing to determine the significance of the results. A small p-value suggests that the observed results are unlikely under the null hypothesis and provides evidence to reject it.

How to calculate lamda for exponential distributions

lamda = 1/mean = inverse of the mean

Typ II fel

låt bli att förkasta nollhypotesen när den är falsk

Z-score

measures the number of standard deviations a data point is from the mean of a dataset. Z-scores are typically used when the population standard deviation is known. They are commonly used in standard normal distribution calculations and in comparing data from different distributions.

Hypergeometric distribution

models the number of successes in a fixed number of draws without replacement from a finite population containing a specified number of successes and failures.

Binomial Distribution

models the number of successes in a fixed number of independent Bernoulli trials, where each trial has the same probability of success.

Exponential Distribution

often used to model the time until the next event occurs in a sequence of independent events that occur at a constant rate

Kvotskala

the highest level of measurement. It has a true zero point, where zero means the absence of the attribute being measured. Examples include height, weight, and income.

When are t-values used

used in situations where the population standard deviation is unknown and must be estimated from the sample, typically in smaller sample sizes.

Multiplikationsregeln

used to calculate the probability of the intersection of two or more independent events

Poisson Distribution

used to model the number of events that occur in a fixed interval of time or space. It's characterized by the fact that events occur independently of each other and at a constant rate.

T-värde

used when the population standard deviation is unknown and is estimated from the sample. T-values are used in t-tests, which are statistical tests for comparing the means of two groups.

When are Z-score used

used when working with a known population standard deviation, especially in cases where data is normally distributed.

Exhaustive variables

variables that cover all possible outcomes or events in a given scenario. In other words, when you have a set of exhaustive variables, every possible outcome must fall into one of the categories represented by those variables. There are no outcomes left unaccounted for

Beskrivande mått för slumpvariabler

väntevärde varians standardavvikelse

When should you use poisson distribution

when modeling the number of events occurring in a fixed interval of time or space.

When should you use binomial distribution

when modeling the number of successes in a fixed number of independent trials.

When should you use exponential distribution

when modeling the time until the next event occurs in a sequence of independent events.

When should you use Hypergeometric distribution

when sampling is done without replacement from a finite population containing a specified number of successes and failures.

Medelvärdet av absoluta differenser (MAD)

är genomsnittetav de absoluta differenserna mellan observationerna ochmedelvärdet

Den centrala gränsvärde satsen (CGS) säger att

stickprovsmedelvärden är normalfördelade om stickproven är tillräckligt stora

Empiriska regeln

0.6826 0.9544 0.9972

Additionsregeln

states that the probability of the union of two or more mutually exclusive events is equal to the sum of their individual probabilities.

Tre fall kring populationsvarianserna när det är två populationer

1. 𝜎1^2 och 𝜎2^2 är kända; standard normalfördelning 2. 𝜎1^2 och 𝜎2^2 är okända men antas lika; 𝑡𝑡-fördelning med df = 𝑛1 + 𝑛2 − 2 3. 𝜎1^2 och 𝜎2^2 är okända men inte antas lika; 𝑡𝑡-fördelning med approximativt df

vi kan välja att kalla en observation en outlier om dess z-score är mer/mindre än

3 eller −3.

Uttömmande (Exhaustive) Event

Om alla möjliga utfall för ett experiment finns blandhändelserna

Ömsesidigt uteslutande (Mutually exclusive) Event

Om de inte har några gemensamma utfall förexperimentet

P-value

Represents the probability of obtaining results as extreme as the observed results, assuming the null hypothesis is true. A smaller p-value suggests stronger evidence against the null hypothesis, leading to its rejection. P-values are used in hypothesis testing to determine the significance of the results.

explain chebyshevs theorem

The theorem states that for any dataset, regardless of its distribution, at least 1−1/𝑘^2 of the data lies within 𝑘 standard deviations of the mean, where 𝑘 is any positive number greater than 1. For example, if 𝑘=2, then at least 1−1/2^2=3/4 or 75% of the data lies within 2 standard deviations of the mean. If 𝑘=3, then at least 1−1/3^2=8/9 or 88.9% of the data lies within 3 standard deviations of the mean.

Typ I-fel

Typ I fel : förkasta nollhypotesen när den är sann

What is MAD (Mean Absolute Deviation)

a measure of the average absolute distance between each data value and the mean of a data set

En binomialfördelad slumpvariabel 𝑋 räknar

antallyckade försök i en serie om 𝑛 försök som är ❑ Oberoende ❑ Sannolikheten för lyckat försök är konstant mellanförsöken

Betingad Sannolikhet

refers to the probability of an event occurring given that another event has already occurred

Obetingad Sannolikhet

refers to the probability of an event occurring without any conditions or prior knowledge

Multiplikationsregeln

sannolikheten att både 𝐴 och 𝐵 inträffar

Kvartilavstånd (IQR)

skillnaden mellan den tredje och denförsta kvartilen (75% respektive 25% av data)

Det viktade medelvärdet beräknas som

𝑥 = Σ𝑤𝑖𝑥𝑖