Probability

Question 1

Probability density plot

Answer 1

Histogram in terms of relative frequency

Question 2

Basic properties of probability

Answer 2

Probabilities are always bound on 0

Question 3

Graphical displays of probabilities

Answer 3

Venn diagram: Classical visual interpretation of probabilities
Probability/Decision trees

Question 4

Conditional probability

Answer 4

Probability is affected by another condition
P(A|B) probability of A occurring, given B has occurred
P(A|B) = P(A∩B) / P(B)

Question 5

Random variable

Answer 5

Variable whose values are generated according to some probability function

Question 6

Types of random variables

Answer 6

Qualitative: Take distinct forms that are non-numeric (like a nominal variable)
Quantitative: Take distinct values that are numeric
Discrete quantitative: Take values that can only assume a countable number of values (integers); ex: # children in household
Continuous quantitative: Takes values that assume both countable and uncountable (non-integer) values; ex: 185.42 cm tall

Question 7

Discrete probability functions

Answer 7

Probability distribution for that variable shows probability of getting each of the distinct levels of that variable

Question 8

Binomial distribution

Answer 8

Used to generate discrete random variables that consist of:
-n random trials
-each of n trials can have 1 of 2 possible outcomes (like flipping a coin)
-each trial is independent of one another
Variable is probability of success
nπ(1-π)
where π is the probability of success

Question 9

Poisson distribution

Answer 9

Commonly used to model counts of events that occur in discrete periods of time or space. Ex: # of children a couple has between 1990 & 2000.
Assumptions of Poisson distribution:
-Events occur 1 at a time (& not at exact same time/place/to the same person)
-Each occurrence at a given time or place is independent
-Expected # of events at any time or place is the same at all times/places
Probability function:
P(y) = (μ^y * e^-μ) / y!
where e is base of natural logarithm ~2.71828
μ is average value of y

Question 10

Distribution functions for discrete data

Answer 10

f(x) = Pr(X=x), probability density function for x
F(x) = Pr(X

Question 11

Continuous probability distributions

Answer 11

Unlike discrete, continuous distributions are defined for (theoretically) an infinite variety of values along the number line.
Probability of observing an occurrence of X at a particular value of x is 0, so we talk about probabilities for continuous variables in terms of intervals
Pr(X = x) = 0
If X is a continuous random variable, and a & b are real constants, then we can calculate the probabilities:
P(Xa), or P(X<b> 0 for -∞ </b>

Question 12

Empirical cumulative distribution function

Answer 12

Cumulative distribution function for real data.

Fn(x) = (#Obs (xi

Question 13

Gaussian, or Normal, distribution

Answer 13

Most frequently used distribution.
Probability density:
f(y) = (1/(SQRT(2πσ))*e^((-(y-μ)^2)/2σ^2)
where μ is the mean and σ is the standard deviation
Normal distribution has mean=0 and variance=1.

Question 14

z-score

Answer 14

Number of standard deviations away from the mean a given value of y.
z = (y-μ)/σ

Question 15

Normal Quantile-Quantile (Q-Q) plot

Answer 15

Normal quantiles represented by straight line & data area the points. A subjective visual test to examine the fit of the line to the data. If the data fit, then “normally distributed”.