Symbols Part 1
X - bar
Complement of Event, G
Gc
The entire collection of objects or outcomes about which information is sought
Population
A subset of the population, containing the objects or outcomes that are actually observed
Sample
A drug for the relief of asthma can be purchased from 5 different manufacturers in liquid, tablet, or capsule form, all of which come in regular and extra strength. How many distinct ways can a doctor prescribe the drug for a patient suffering from asthma?
30 ways
sample median
x-tilde
Variance of random variable, K
V[K]
When we divide the population into subpopulations, then we randomly select individuals from each of the subpopulations
Stratified Random Sampling
A sample where every subject in the population has the same chance of being selected.
Simple Random Sample
Mr. and Mrs. Joe are members of an organization with 5 women and 4 men, including themselves. The organization needs to appoint a committee. How many ways are there to form the committee if the committee has 5 people.
9 people choose 5 people = 126
expected value of a random variable, Z
E[Z]
Intersection
n
A study were individuals in a sample are measured without being affected
Observational Study
Researchers assign individuals to groups and apply different treatments to each group.
Experimental study
Mr. and Mrs. Joe are members of an organization with 5 women and 4 men, including themselves. The organization needs to appoint a committee. How many ways are there to form the committee if the committee has 5 people, 3 of whom must be women, and 2 must be men?
5 choose 3 X 4 choose 2 = 60
U
Binomial coefficient
n choose k
Is a measure of symmetry (or lack of symmetry)
Skewness
_________ statistic, its value does not change much when an outlier is added or removed from a sample.
Robust
Hailey loves hosting wine-tasting parties. Her current supply includes nine (9) bottles of Zinfandel, eight (8) bottles of merlot, and twelve (12) bottles of Cabernet, all from different wineries.
Hailey wants to serve three bottles of Zinfandel out of her nine bottles of Zinfandel collection to her friends. When tasting wine, Hailey knows that the serving order matters. How many ways are there to serve three bottles of Zinfandel out of her nine bottles of Zinfandel to her friends?
9 X 8 X 7 = 504
Probability Density Function of X
f(x)
Cumulative Density Function of X
F(x)
A phenomenon where two different samples from the same population may be vastly different from each other
Sampling variation
Numerical summaries of a population
Population Parameter
Hailey loves hosting wine-tasting parties. Her current supply includes nine (9) bottles of Zinfandel, eight (8) bottles of merlot, and twelve (12) bottles of Cabernet, all from different wineries.
Hailey wants to give away three bottles of wine from her collection to her friends. Thus, she walks into her wine cellar and randomly grabs three bottles of wine where the order of grabbing the wine bottles does not matter. How many ways can she choose all three bottles of wine from the same type of wine?
9 choose 3 + 12 choose 3 + 8 choose 3 = 360