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STAT 371: Stats 371 I
Sample |
a representation to the target population. |
Populations |
the entire collection of individuals or units that a researcher is interested in |
parameter |
a quantity describing a population. constant and unknown |
random sample |
should be accurate and precise |
accurate |
unbiased |
precise |
precise |
convience bias |
collects items only be convience |
volunteer bias |
behavior/opinions affects whether they are sampled |
Categorical |
qualitative variable |
nomial |
variety
-no order |
ordinal |
categories have an inherent order |
Numerical |
quantitative value |
discrete |
whole numbers |
continuous |
can be any measurement |
response |
are considered outcomes
-dependent |
explanatory |
thought to potentially affect outcomes
-independent |
IQR |
the inter quartile range= a range between the 1st and 3rd quartiles |
mean |
is more sensitive to extreme values |
median |
more resistant to extremes. Used as middle value of boxplot |
standard deviation |
the square root of sample variance |
sample variance |
the sum of squared deviations
-variation from mean |
Elementary outcome |
the complete description of a single result from the exeriment |
sample space |
the entire group of elementary outcomes |
intersection |
"A&B" consists of outcomes in both A and B |
Union |
"AorB" consists of outcomes in either A, or B, or both |
Complement |
"NotA" consists of outcomes that are not in A |
Mutually exclusive |
events that have no common elementary outcomes (can't happen simultaneously) |
A or B |
P(A)+ P(B) |
Conditional probability |
the probability of event A given B, is the probability of A given that B occured |
A/B |
P(A&B)/P(B) |
A and B |
P(A/B) X P (B) |
independent events |
if occurrence of one event does not affect the chance that the other will happen |
B/A |
(P(A/B) X P(B))/(P(A/B)XP(B)+P(A/notB)XP(notB) |
random variable |
is a variable that depends on outcomes of a chance situation. |
probability distribution |
one Random Variable should assign probability to all values of the Random Variable |
My |
E(y)=Sumy=(P(Y=y))
p(y=0)+p(y=1) |
Variance (θ²y) |
E(Y-M)²=Sum((Y-M)²)*P(Y=y)) |
Standard Deviation (θ) |
√Sum((Y-M)²)*P(Y=y)) |
My |
αMx+B |
standard deviation |
/a/θx |
Binomial distribution |
weighted distributions of probability
y-Bin(n,p) |
Bin |
probability of getting J successes
-(nj)p^j(1-p)^(n-j) |
Assumptions |
-trials have exactly 2 outcomes
-probability of success (p) is same for all trials
-# trials, n, is fixed in advance
-all trials are INDEPENDENT |
normal distribution |
-many random varaible have bell shaped distribution
-normal density curve is a good approximation
-analytical form of bell curve |
N (normal) |
y-n(My,θy)
-symmetric around its mean
-single node
-probabilty density highest at mean
-probability measured by area under curve |
Z |
indexes a number of standard deviations from the mean |