Topic 5: Probability and Basic Statistic Theory Flashcards
(18 cards)
Empirical Relative Frequency Distribution
In a frequency table, the emperical relative frequency is the probability of an event E, such as an interval in your table, is to happen:
P(E) = f/N
where f is the frequency of E
Joint probability
Probability of being in two categories simultaneously.
Conditional probability
The probability that depends on previous events.
Bivariate frequency table
This is an example of a _______ probability.
How do we calculate it?
This is an example of a joint probability.
We just have to take any entry for which we want the probability and divide by N.
This would be illustrated by the intersection of two events E_1 and E_2.
Conditional probability formula
P(A intersection B) = P(A)P(B|A) = P(B)P(A|B)
Permutations without replacement
n!
You place the first one (n choices), then the second one (n-1 choises), etc.
n*(n-1)*…*1
Permutation of n objects in r boxes
nPr = n!/(n-1)!
Combinations
Order does not matter:
nCr = n!/(r!(n-r)!)
Binomial Events
Two events are mutually exclusive. This means that if one happens, the other can’t happen.
Probability Distributions
- Discrete
- Continuous
- Binomial
Binomial distribution
Criteria:
- Binomial events
- Interested into P( r successes in n trials)
- Trials have to be independent
- P(success) is the same in each trial
Binomial distribution formula
P(r,”success”) = nCr(p^r)(1-p)^(n-r)
The population mean outcome for n trials
mu = np
Variance of outcomes for n trials
sigma = np(1-p)
Standard deviation of outcomes for n trials
square root of sigma
=
square root of (np(1-p))
Normal distribution
p = ( 1 - p ) = 0.5
As n increases, the curve is smoother
mu is the point where the curve peaks
sigma is the amount between two values on the x-axis
The area under the curve is the probability
The y-axis is the probability density
Do example on slide 19, topic 6
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