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Stats Test 1 - "It's all intuitive." > Discrete (specific) probability laws > Flashcards

Discrete (specific) probability laws Flashcards

1
Q

A list of a variable’s values also with the probability of their occurrence is…?

A

A probability distribution

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2
Q

What is a probability density function (PDF)?

A

It is a function that describes the probability density at each point in a sample space.

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3
Q

Probability laws are?

A

Functions that define probability laws

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4
Q

What are the major types of distributions (of probability)?

A
  1. Empirical 2. Theoretical 3. Discrete 4. Continuous
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5
Q

Empirical are

A

values of varibale are collected through empirical observation

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6
Q

Theoretical are

A

values of variable are derived from mathematical function

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7
Q

Discrete are

A

Values of a variable that are countable

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8
Q

Continuous are

A

Values of variable exist along a continuum the discrimination between discrete and continuous can sometimes be arbitrary

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9
Q

How to we hope to apply distributions (of probability)?

A

By knowing how closely a frequency distribution from a sample (empirical distribution) matches a theoretical probability distribution from some corresponding population.

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10
Q

What are the two types of probability?

A

Theoretical probability and empirical probability

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11
Q

Describe theoretical probability

A

It is deductive (a priori – which means with prior knowledge) Looks into the future possibilities # of favor outcomes divided by total # of outcomes

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12
Q

What is an example of a theoretical probability?

A

the probability of a face card in a random (normal 52 card deck)? We already know the distribution of cards and all the outcomes therefore based on this knowledge (a priori) we are able to come up with a theoretical probability.

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13
Q

What is empirical probability?

A

Inductive (a posterior) relative frequency of past events # of times an event occurred divided by the total # of trials

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14
Q

What is an example of empirical probability?

A

probability of rain on August day in Albuquerque? We look at the historical data (a posterior) to determine the events that occurred and therefore compute a probability of future events occuring.

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15
Q

What are five important theoretical probability distributions for behavioral research?

A
  1. Discrete Binomial 2. Continuous normal, t, x2, F
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16
Q

What is the granddaddy of all distributions?

A

The normal distribution, more or less most distributions are related or rely on the normal distribution.

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17
Q

What is a formula that gives the probability of some sample statistic having a specific value?

A

A probability law

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18
Q

What is another way to think of a probability law?

A

A specific method for selecting entities in a population given some characteristic.

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19
Q

How do we define specific probability laws?

A

a random sample of n observations is taken from a population containing N units, each of which belongs tone and only one of K categories, the categories being, in effect the possible values that an observation may have.

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20
Q

What are two key questions we have about probability laws when they are defined?

A

How is sampling done? what is the nature of the categories in the population?

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21
Q

There can be two different types of sampling methods

A
  1. Depletable – sampling without replacement and N is finite 2. Undepletable - sampling with replacement OR N is infinite
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22
Q

What are different types of population categories?

A
  1. each unit belongs to only one category (therefore the categories are mutually exclusive) 2. each unit must belong to a category (therefore the categories are exhaustive) If you have 1. and 2. then you have a partition Finally, the number of categories in a population 2 = dichotomy 3+ = multichotomy
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23
Q

Given this framework what are the 4 distinct probability laws?

A
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24
Q

What is hypergeometric probability law?

A

a random sample of n observations is to be drawn without replacement from a finite population (depletable).

The population contains n units each of which belongs to one or the other of two mutually exclusive and exhaustive categories. (dichotomy of units)

25
Q

How do statisticians typically call this dichotomy (with hypergeometric probability?

A

As successes and failures

This is an arbitrary distinction

Successes are usually called “R”

Failures are expressed as “N-R”

26
Q

How is the hypergeometric probability law expressed?

A
27
Q

What is this an example of?

A

A hypergeometric probability type of question.

28
Q

How can we generalize the hypergemoetric law so that it is now multivariate?

A

This means there are more than two distinct categories (mutlichotomy)

29
Q

What does this formula express?

A

Hypergeometric multivariate formula.

30
Q

“At least” is special in proabilities, why?

A

It means “x or more”

31
Q

What means “X or less” in word problems for probability?

A

“no more than X”

32
Q

When word problems involve “at least” OR “ no more than” how do we obtain an overall probability?

A

One must add up the probabilities of each occurence.

33
Q

An undepletable probability law is called?

Hint: it is the most famous probability law in all of statistics

A

The binomial probability law

34
Q

What are the signficant attributes of the bionmial probability law?

A
  1. the outcomes of the individual observations are independent of each other.
  2. every unit belongs to one or the other of two mutually exclusive and exhaustive categories
  3. population is a dichotomy
  4. the sampled population is INFINITE
35
Q

How are successes and failures expressed in the binomial probability law?

A

The proportion of units belonging to one category are labled as successes = “p”

The other proportion are labeled as failures “1-p”

36
Q

What probability law is being expressed here?

A

The binomial probability law

37
Q

What kind of probability law can be used to solve this equation?

A

The binomial probability law.

38
Q

A generalization of the binomial probability law to the cae where the sample population contains more than two kinds of units is called what?

A

Multinomial probability law

39
Q

A random sample of n observations is to be drawn either from an infinite population or with replacements from a finite population. And the outcomes are independent of each other

What law should we use?.

A

Either the binomial or multinomial (depending on the number of categories).

40
Q

How is the multinomial probability law expressed?

A
41
Q

What probability law would we use to solve this word problem?

A

Multinomial probability law

42
Q

If I want to find the probability that a sample of n
observations will have to be taken in order to
obtain a predetermined number r of successes, which probability law should I use?

–this an infinite population

A

The negative bionmial probability law

“How many trials will it take before we get N successes”

43
Q

How does one determine the probability that the rth success will occur on the nth observation (given an infinite population)?

A

The negative binomial probability law

44
Q

What law is expressed here?

A

The negative binomial probability law

45
Q

Write out the negative binomial probability law.

A
46
Q

Write out the binomial probability law.

A
47
Q

Write out the hypergeometric probability law

A
48
Q

Write out the hypergeometric multivariate probability law

A
49
Q

Write out the multinomial probability law

A
50
Q

What kind of probabilty law would we use to solve this word problem?

A
51
Q

We need a special case of the negative bionmial when the r=1, what is this called?

A

Geometric probability law

52
Q

How is the geometric probability law applied?

A

Under the same conditions as the negative binomial probability law and therefore the binomial probability law

53
Q

Write out the geometric probability law

A
54
Q

Which probability law is expressed here?

A

Geometric probability law

55
Q

What type of probability law solves this word problem?

A

Geometric probability law

56
Q

IF we have N pairs of matched observations, we can ask whetehr the distribution ofone set of numbers is different in magnitutde from the otehr set of numbers.

What type of probability law is used?

A

The sign test which is a simple application of the binomial probabibilty law.

57
Q

For the sign test, what do we assign as the default probability?

A

0.5 for success or failures, this implies that there is no greater than a equal chance for change and the distribution of variables will be normal about some mean. Therefore a deviation from this mean will be greater than chance regardless of the direction.

58
Q
A

Stats Test 1 - "It's all intuitive." (4 decks)

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