Probability Flashcards
Probability
number of ways to get desired outcome / total possible outcomes
Compound Events
a combination of simple events (ie: rolling two dice or flipping a coin three times)
Permutations: How many different ways can we arrange x items out of n in which order matters?
If no repetition is allowed, use: n! / (n-k)! If repetition is allowed, used: n^x
Combinations: How many ways are there to arrange x items out of n in which order does NOTmatter?
n! / (n-x)!x!
In how many unique orders can 5 horses finish a race? (hint: combination because order does not matter)
5! 5x4x3x2x1
Look for permutations anytime order…
matters
Look for combinations anytime order…
does not matter
Enumeration
writing it out
Factorial
n! n x n-1 x n-2…
Conditional Probability of disjoint independent events (ie: rolling an odd number or a 4 on one die)
P(A or B) = P(A) + P(B)
Conditional Probability of non-disjoint independent events (ie: choosing a spade or a jack)
P(A or B) = P(A) + P(B) - P (A and B) subtract the overlap
Complement (of any event, A)
The probability of A not happening
If two events are DISJOInT ie: rolling an odd number or a 4 on one die?
Add the two events Ie: 1/2 + 1/6
Joint Probability
The probability of the intersection of two events (probability that both events occur)
Independent events
The probability of one is not affected by whether the other event occurred
Mutually exclusive events
Cannot happen at the same time
Conditional probability
Event A happening depends on if B happens
Normal distribution model
68% within +-1 standard deviations of the mean 95% within +-2 standard deviations of the mean 99.7% within +-3 standard deviations of the mean
Z-score (standard value)
Way to compare an event y to the mean y^-
Normal Model / Bell Shaped curve %’s
68% w/in 1 st dv
95% w/in 2 st dv
99.7% w/in 3 st dv
The normal model is more bell shaped and symmetrical with more…
data
what does a Z-Score do?
compares things in totally different groups (apples to oranges)
Higher Z-Score compared to lower Z-Score
A Z-Score of 3 is VERY far above the mean, whereas a Z-Score of 0.2 is just above the mean
Z-Score equation
Z = (y-y’)/st dev or diff/st dev
What is Expected Value?
An estimate of the mean calculated by the weighted average of all possible values. Weights are the probabilities.
Variance
a measure of dispersion - it tells us how far a set of values spread out from each other and how far each value is away from the mean
How do you calculate the variance?
sum of variances/number of instances
Shows 5 stats:
Min Score, Max Score, and three percentiles
What is population?
Population is all items of interest, and has Parameters (ie: mean and standard deviation)
What is a Sample?
A sample is a subset of the population, and has statitstics
What is a survey?
A sampling of facts, figures, or opinions used to approximate something about a population. A good survey sample should be random and representative.
Simple Random Sampling (SRS)
Every possible sample of n individuals is equally likely to be selected
What is Linear Regression?
A facy name for the line of best fit
A techinique by which one dependent variable (y) is regressed againsted one independent variable (x), and the relationship between the two is in the form of a straight line.
What are the linear regression variables?
y = dependent variable
x = independent variable
What is a Chi-Squared value?
Looks at frequencies. Goodness of fit test. Do the values have a lot of deviation from the expected outcome? The null hypothesis is accepted or rejected.
How do you calculate the Chi-Squared value?
The sum of (observed - expected)^2 over expected
What is the R coefficient?
The correlation coefficient. Measures how close the data are to the fitted regression line. The closer to 1 (pos correlation) or -1 (neg correlation), the better the fit
