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UNI.YEAR1.TERM1.INTROTOSTATS > probability and probability distribution > Flashcards

probability and probability distribution Flashcards

1
Q

what is the frequentist view ?

A

the proportion of trials in which an outcome occurs, calculated as the no of trials approaches infinity

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2
Q

what is the subjective view ?

A

someones subjective belief about somethings likelihood. however, adjusted in light of evidence.

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3
Q

what is an axiomatic approach ?

A

where you ignore the actual problem and just examine the numbers. there is no mention if fairness

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4
Q

define these probability question terms

a. experiment
b. sample space
c. trial
d. event

A

a. an activity with a range of outcomes
b. all possible outcomes
c. a single performance of the experiment
d. one of the possible outcomes

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5
Q

what is the complement of P(A) ?

A

P(not A)

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6
Q

what are the basic rules of probability ?

A

0 < P(X) < 1

sum of P = 1, for all outcomes

P(not A) = 1 - P(A)

P(A or B) = P(A) + P(B)

P (A and B) = P(A) x P(B)

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7
Q

what is the notation for

a. P(A or B)
b. P(A and B)

A

a. P(AUB)

b. P(ANB)

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8
Q

what does mutually exclusive mean ?

A

two events cannot happen simultaneously

e.g. a marble cannot be square and round

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9
Q

what are independent variables ?

A

when the first event has no effect on the second event’s probability.

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10
Q

what are dependent variables ?

A

when the first event has an effect on the second event’s probability.

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11
Q

when events A and B are not mutually exclusive, how do you calculate P(AUB) ?

A

P(A) + P(B) - P(ANB)

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12
Q

what is

a. marginal probability
b. union probability
c. joint probability
d. conditional probability

A

a. just plain probability of one event by itself P(A)
b. P(AUB)
c. P(ANB)
d. the probability of one event given that another event has already happened P(A|B)

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13
Q

how do you calculate conditional probability ?

A

P(A|B) = P(ANB)/P(B)

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14
Q

how can you tell if two events are independent ?

A

rearrange the conditional probability equation to :
P(ANB) = P(A) . P(A|B)
and the two event are only equal when this is true

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15
Q

to do combination probability we must be able to count the number of outcomes. what are the two types of combination probability, and what do they mean ?

A
  1. combination - order of elements in outcomes doesn’t matter
  2. permutation - order of elements in outcome does matter
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16
Q

how do you calculate the number of : ( combinations with replacement ) ?

A

N^r

n = number of options of elements
r = number chosen
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17
Q

how do you calculate the number of : ( combinations without replacement ) ?

A

nPr = n! / (n-r)!

n = number of options of elements
r = number chosen
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18
Q

how do you calculate the number of : ( permutations with replacement ) ?

A

nCr = (r + n - 1)! / (r)! . (n -1)!

n = number of options of elements
r = number chosen
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19
Q

how do you calculate the number of : ( permutations without replacement ) ?

A

nPr = n! / (r)! . (n-r)!

20
Q

what is bayes theorem ?

A

when there are false positives and false negatives

pregnancy example

Pr(P|+) = Pr(PN+) / Pr(PN+) + Pr(NPN+)

21
Q

what is bayesian updating ?

A

when you have a prior possibility (posterior possibility e.g. probability of being pregnant before the test is even taken)
you use bayes rule to calculate the posterior possibility when there is new info

22
Q

what is the bayes rule ?

A

Pr(A|B) = Pr(ANB) / Pr(ANB) + Pr(NANB)

23
Q

what types of probability distribution are there ?

A 
normal 
poisson
binomial
cumulative binomial
uniform
24
Q

what are probability distributions ?

A

each outcome in the sample space has a probability - this displayed is call the probability distribution

  • they can be discrete or continuous.
  • probability and range of outcomes may still be known
  • can take on any value in the potential outcomes
25
Q

what are binomial probability distributions?

A

they are a family of probability distribution

- two parameters: n , p

26
Q

name the characteristics of a binomial distribution ?

A 
. n no of trials
. trials are independent
. only 2 outcome possibilities
. one outcome labeled success
. Pr ( success ) = P
. Pr ( failure ) = 1 - P
. P doesn't change between trials
. r = no of successes
27
Q

in a binomial distribution what is the Pr( r ) ?

A

nCr . P^r . (1-p)^(n-r)

28
Q

in a binomial distribution what is the mean ?

A

E(r) = n x p

29
Q

in a binomial distribution what is the variance ?

A

v(r) = E[ (r-mean) ^2 ] = sum of (r-mean) ^2 x p = n . p . (1-P)

30
Q

how do you calculate cumulative binomial distribution ?

A

Pr( r < C ) =

Pr( r = 0 ) + … Pr ( r = c )

or find the statistical table for the distribution and look up the Pr

31
Q

describe a poisson distribution ?

A
  • two possible outcomes
  • repeated finite no times
  • p of ‘ success’ is the same every time
  • it is the probability of very rare event
32
Q

how do you calculate the probability of a success in a poisson ?

A

P(X) = (mean^X) . ( e^ -mean) / X!

33
Q

compare binomial and poisson distribution ?

A
  • binomial : discrete data, finite support

- poisson : data goes to infinity, no finite support

34
Q

what is uniform distribution ?

A

continuous data all in one solid block of even probability, you can’t calculate the probability of just one event

distribution area = 1
and the area goes on the x axis from a to b

35
Q

in a uniform distribution, how do you calculate the probability of each event ?

A

f(x) = 1/b-a

36
Q

in a uniform distribution, how do you calculate the mean ?

A

mean = a+b / 2

37
Q

in a uniform distribution, how do you calculate the variance ?

A

(b - a) ^2 /12

38
Q

in a uniform distribution, how do you calculate the standard deviation ?

A

(b - a) / ROOT[12]

39
Q

name the types of continuous probability distributions ?

A
  1. normal ( gaussian ) distribution
  2. cummulative distribution function
  3. linear combinations of random variables
40
Q

describe the normal ( gaussian ) distribution ?

A

pr sort of (x) =
F(X) = 1/ standarddev . rot[2pie]
all times by e^ -1/2(x-mean/sd)^2

41
Q

how do you calculate the mean in a normal ( gaussian ) distribution ?

A

the mean is half of the probability mass

42
Q

where is the majority of the distribution in ?

A

within 3 sd either side of the mean.

43
Q

where of the x axis of a normal distribution graph is this

a. Pr(a > z)
b. Pr(a < z)
c. Pr(a < z < b)

A

a. to the right of Z
b. to the left of Z
c. in between Za and Zb

44
Q

what is f(x) for the cumulative distribution function ?

A

(1/root{2pie}) x e^(-1/2 )xX^2

45
Q

what is Y for a linear combination of random variables ?

A

Y = W1.X1 + W2.X2

46
Q

what is the …… for a linear combination of random variables ?

a. expected value ( mean )
b. variance of each
c. variance overall

A

a. same added
b. same added
c. same times by W^2 added

47
Q

describe joint probabilities?

A

joint probability Pr ( X=x,Y=y)

the sum = 1

the marginal probability would now be the sum of all the options where X=x and y = whatever

UNI.YEAR1.TERM1.INTROTOSTATS (5 decks)

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