STT. Exam 2 Flashcards
conditional probability formula
=Pr(little |big)
false positive:
test states the condition is present, but it is actually absent
false negative:
test states the condition is absent, but it is actually present
sample space
“S”, set of all possible outcomes
law of large numbers
the larger the number of trials, the more stable the probability will become
independent trials
outcomes do not affect each other
event
subset of sample space, ex. A {2,4,6}
probability
count in event (ex. A)/ total in S
probability is between two numbers:
0 and 1
certain event
the probability of an event that must occur, is 1
not A:
event that A does not occur
A and B:
both A and B occur (what overlaps!)
A or B:
event that both occur (don’t count overlap twice)
disjoint/mutually exclusive A and B means that:
they have no overlap
disjoint/mutually exclusive A and B formula:
P(A or B)= P(A and B) or P(A) + P(B)
A and B formula when trials are independent:
P (A and B)= P(A) x P(B)
complement rule:
P(not A or A compliment)= 1- P(A)
If A and B are disjoint, then…
P(A and B) = 0
If Pr(A and B) do not equal 0, then…
A and B are not disjoint
or=
add
and=
multiply
if A and B are independent, then:
P(A and B) = P(A) x P(B)
marginal
looking at columns, going “down”
conditional
looking at rows, going “across”
if A and B are dependent, then:
Pr(A and B) = Pr(A) x Pr(B|A)
Pr(A and B) = Pr(B) x Pr(A|B)
X=
random variable
E(X)=
expected value, mu, population mean
population mean notation:
mu
population SD notation:
sigma
sample mean notation:
x bar
sample SD notation:
s (little s)
important property of density curve:
areas under the curve correspond to relative frequencies
SD rule:
68% is 1 SD away
95% is 2 SD away
99.7% is 3 SD away
z-score formula:
x-xbar/SD
chap. 6 z-score formula:
x-mu/sigma
68% of data:
mu + or - sigma
95% of data:
mu + or - 2sigma
99.7% of data:
mu + or - 3sigma
center:
mu
spread:
sigma
area under the density curve represents the:
probability
normal distribution/ ‘N’ formula:
= N(center, spread)
=N(mu, sigma)
standard normal notation for mu:
0
standard normal notation for sigma:
1
x follows what notation:
general normal, x=N(mu, sigma)
z follows what notation:
standard normal, z= N(0,1)
lower tail:
to the left
upper tail:
to the right
what tail is used to find percentiles?
lower tail (to the left)
population proportion:
p
sample proportion:
p-hat
sigma of p-hat formula:
square root of p times 1 - p-hat, all over n
SD rules for p-hat:
68%= p + or - SD formula
95%= p + or - 2 times the SD formula
99.7%= p + or - 3 times the SD formula
z-score p-hat formula=
= p-hat - p/ SD formula
sampling distribution notation for p-hat=
= N(p, SD formula)
