Everything you need to know for the BSip course for the pre-master Accountancy at Nyenrode Business University. Per chapter, the theory is covered with many examples and exam questions + answers. I have succeeded this course with this summary easy in one go.
Statistics Summary of Book "Business Statistics in Practice"
Summary Business Statistics
Samenvatting Business Statistics in Practice (BSiP) voorjaar 2021 Pre-master Accountancy
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Nyenrode Business Universiteit (Nyenrode)
Accountancy
Business Statistics in Practice (BSIP)
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BSiP
Hoofdstuk 4 Probability & sample spaces
4.1 probability, sample spaces and probability models
Probability: the likelihood of the event to occur (nummer tussen 0 en 1)
Performing statistical studies:
- Performing a controlled experiment Experiment = any process that
- Observing uncontrolled events generates well-defined outcomes
Sample space = the set of all possible outcomes for the experiment
- Experimental outcomes
- Sample space outcomes
The probabilities for each event can be assigned in different ways:
- Classical method
o (equal possibilities) – dobbelsteen, kop of munt
- Relative frequency method
o (based on historical data) – hoe vaak je na je werk in de file komt te staan
- Subjective method
, o (using “expert” judgement) – manager vragen over de verkopen volgend jaar
Eerste twee worden voornamelijk bij dit vak gebruikt
Relative frequency method → long-run relative frequency interpretation
Kop of munt prob = 0,5. Kan voorkomen → 6/10, 47/100 etc. Maar hoe vaker de munt wordt
gegooid (als we de munt een oneindig groot aantal keren opgooien), zal de relative frequency
steeds dichter de 0,5 benaderen.
= mathematical idealization
Dus wanneer experiment wordt uitgevoerd volgens relative frequency method zijn kansen niet
gelijk, maar wanneer experiment oneindig wordt uitgevoerd benaderd de kans de uitkomst volgens
de classical method.
Subjective method: Wanneer het experiment niet veelvoudig kan worden uitgevoerd wordt de
kans geschat o.b.v. previous experience with similar situations, intuition judgement or special
expertise.
Probability model = a mathematical representation of a random phenomenon (vb = experiment),
bestaat uit:
1. Sample space of the experiment
2. Procedure for calculation probabilities concerning the sample space outcomes
Een ander type random phenomenon = random variable (variable whose value is numeric and is
determined by the outcome of an experiment)
The probability model describing an random variable is called a probability distribution, bestaat
uit:
1. Specification of the possible values of the random variable
2. A table, graph, or formula that can be used to calculate probabilities concerning the values
that the random variable might equal.
Twee typen probability distribution:
- Discrete probability distributions
o Binomial distribution (model)
o Poisson distribution (model)
- Continuous probability distribution
o Normal distributions (model)
o Exponential distribution (model)
Ieder probability model is gebaseerd op een of meer veronderstellingen over het random
phenomenon (equally likely sample space outcomes OF sample space outcomes associated with the
possible occurrences of independent events.
4.2 Probability and Events
Event = a set of one or more sample space outcomes
The probability of an event is the sum of the probabilities of the sample space outcomes that
correspond to the event.
,Wanneer all of the sample space outcomes are equally likely, than the probability that an event will
occur is equal to the ratio:
The number of sample space outcomes that correspond to the event
The total number of sample space outcomes
4.3 Some Elementary Probability Rules
Rule of complements:
Als A een gebeurtenis is, is de complement van A de gebeurtenis dat A niet zal
plaatsvinden. P(𝑨) = the probability that A will not occur
P(A) + P(𝐴) = 1 OF P(𝐴) = 1 – P(A)
Intersection of two events:
De gebeurtenis die optreedt als zowel gebeurtenis A als gebeurtenis B tegelijkertijd plaatsvinden. P(A
∩ B) = the probability that both A and B will simultaneously occur.
Contingency Table summerizes the events.
Union of two events:
De gebeurtenis die optreedt wanneer gebeurtenis A of gebeurtenis B (of beide) plaatsvindt.
P(A ∪ B) = the probability that A or B (or both) will occur.
Additional rule:
The probability that A or B (or both) occur =
P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
Als je P(A) en P(B) namelijk bij elkaar optelt tel je mogelijkheid
AB en BA twee keer, terwijl dit maar één keer moet. Daarom haal
je een keer P(A ∩ B) eraf.
Mutually Exclusive events:
Gebeurtenissen die niet overeenomsten hebben in de sample
space en hierdoor niet tegelijkertijd kunnen voordoen. Als 2 events mutually exclusive zijn, hebben ze
geen overlapping en is de kans dat beide zich voordoen 0.
P(A ∩ B) = 0
The addition rule for two mutually exclusive events:
A en B zijn mutually exclusive events.
Then, the probability that A or B will occur
= P(A ∪ B) = P(A) + P(B)
The addition rule for N Mutually Exclusive Events
Als A1, A2, .. AN are mutually Exclusive if no two of the events have any sample space outcomes in
commn. In this case, no two of the events can occur simultaneously
P(A1 ∪ A2 ∪ … AN) = P(A1) + P(A2) + … + P(AN)
, 4.4 Conditional Probability and Independence
Conditional probability: de kans dat een event zich voordoet terwijl we al weten dat de andere event
al is voorgedaan. Dus wat is de kans dat A zich voordoet als B al is voorgedaan en gegeven. In de
formule betekent dit: wat is de kans dat A en B beide zich voordoen / de kans op B die al gegeven is.
The probability of the event A, given the condition that the event B has occurred, is written as P(A|B)
– the probability of A given B. the conditional probability of A given B.
- Probability of event A given that event B has occurred P(A|B)
o P(A|B) = P(A ∩ B)
P(B)
- Probability of event B given that event A has occurred P(B|A)
o P(B|A) = P(A ∩ B)
P(A)
P(H|E) = kans op een hoog (H) nummer gegeven dat het een even (E) nummer is.
P(H|E) = P(H ∩ E) = 1/6 = 1/3
P(E) 1/2
P(E|H) = de kans op een even (E) nummer gegeven dat het niet een hoog (H) nummer is.
P(E|HC) = P(E ∩ Hc) = 2/6 = 1/2
P(Hc) 4/6
General multiplication Rule – Two ways to calculate P(A ∩ B)
P( A ∩ B) = P(A) * P(B|A)
= P(B) * P(A|B)
Independent events
Two events are independent if and only if: (het maakt niet uit of een ander event is geweest of niet)
1. P(A|B) = P(A), or
2. P(B|A) = P(B)
P(A|B) = P(A) als het niet uitmaakt of event B heeft plaatsgevonden.
Club A heeft kans op 0,5 om te winnen en club B een kans op 0,65. Ze spelen niet tegen elkaar. Club
A winst, dan heeft club B nog steeds 0,65 kans om te winnen → independent
Multiplication Rule for two independent events
Als A en B independent events zijn:
P( A ∩ B) = P(A) * P(B)
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