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Statistics for Psychologists 1
Week 1
Subject: Probability theory and random variables
Literature: chapter 4 (not including the 'Beyond the basics' paragraphs and the
paragraph on Bayes’s Rule on p.301)
237-311
Randomness
Random – regular distribution of uncertain outcomes
Probability – the proportion of times that outcome would occur in a long
series of repetitions
To have randomness you must have a long series of independent trials that do
not effect one another.
Probability Models
In a probability model there is a sample space and an probabilities
Sample Space (S) - The set of all possible outcomes
Event – Outcome or a set of outcomes
When assigning probabilities, it is written like this:
P(A) = the probability of the event A occurring
Ac = events that consist of the outcomes that are NOT A
Disjoint events are when events have no outcomes in common
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Independent events are when one event doesn’t change the probability
assigned to another event.
Rules of probability:
1.
The probability of any event will fall into 0 ≤ 𝑃(𝐴) ≤ 1
2.
All possible outcomes must = 1
3. The addition rule for disjoint events
If 2 events are disjoint then they have no outcomes in common
P(A or B) = P(A) + P(B)
4. The complement rule
the complement of an event that dose not occur that event is written as Ac
5. The Multiplication rule
If events A and B are independent
P(A And B) = P(A)P(B)
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Random Variables
Random Variable – This is a variable that has a numerical value that is
determined by the probability of the outcome of the variable.
There are two types:
Discrete Random Variable – Is a variable that has a limited number of possible
values
It is discrete because X can only be isolated points in a number line
e.g. tossing a line X is the number of heads, X can only equal a finite number of
thing, like 1 head, 2 head, 3 heads
Continuous Random Variables – Is a variable that can take on non-finite
values, for example the test results.
A density curb shows the probability distribution of this continuous random
variable
Means and Variances of Random Variables
Probability Distribution – this is a graphical method used to show the
distribution of P(A)
It has a mean and a standard deviation
Variance - The average of the squared differences from the Mean
To calculate the Variance, take each scores difference from the mean, square
it, and then average the result.
Standard deviation – Shows how spread out the data is in relation to the mean
= the square root of the variance
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Statistics for Psychologists 1
Week 1
Subject: Probability theory and random variables
Literature: chapter 4 (not including the 'Beyond the basics' paragraphs and the
paragraph on Bayes’s Rule on p.301)
237-311
Randomness
Random – regular distribution of uncertain outcomes
Probability – the proportion of times that outcome would occur in a long
series of repetitions
To have randomness you must have a long series of independent trials that do
not effect one another.
Probability Models
In a probability model there is a sample space and an probabilities
Sample Space (S) - The set of all possible outcomes
Event – Outcome or a set of outcomes
When assigning probabilities, it is written like this:
P(A) = the probability of the event A occurring
Ac = events that consist of the outcomes that are NOT A
Disjoint events are when events have no outcomes in common
Find more resources on this topic on
,dmuwodmfdmuwodmfdmuwodmf-8d950e67cdb52312aa9bdffcf53db9dd
Independent events are when one event doesn’t change the probability
assigned to another event.
Rules of probability:
1.
The probability of any event will fall into 0 ≤ 𝑃(𝐴) ≤ 1
2.
All possible outcomes must = 1
3. The addition rule for disjoint events
If 2 events are disjoint then they have no outcomes in common
P(A or B) = P(A) + P(B)
4. The complement rule
the complement of an event that dose not occur that event is written as Ac
5. The Multiplication rule
If events A and B are independent
P(A And B) = P(A)P(B)
Save time with the right summary on
, dmuwodmfdmuwodmfdmuwodmf-8d950e67cdb52312aa9bdffcf53db9dd
Random Variables
Random Variable – This is a variable that has a numerical value that is
determined by the probability of the outcome of the variable.
There are two types:
Discrete Random Variable – Is a variable that has a limited number of possible
values
It is discrete because X can only be isolated points in a number line
e.g. tossing a line X is the number of heads, X can only equal a finite number of
thing, like 1 head, 2 head, 3 heads
Continuous Random Variables – Is a variable that can take on non-finite
values, for example the test results.
A density curb shows the probability distribution of this continuous random
variable
Means and Variances of Random Variables
Probability Distribution – this is a graphical method used to show the
distribution of P(A)
It has a mean and a standard deviation
Variance - The average of the squared differences from the Mean
To calculate the Variance, take each scores difference from the mean, square
it, and then average the result.
Standard deviation – Shows how spread out the data is in relation to the mean
= the square root of the variance
Discuss this document with others on
