Probability

Question 1

Memorise probability chapter summaries (This isn’t even necessary anymore, I just originally couldn’t even be bothered to make proper flashcards for prob.)

Answer 1

Trial exams all finished but you have that stupid maths non calc one in class tomorrow, went to a Borneo final information evening in the city last night and today I should be studying all day but I’ve already watched an episode of Gotham and I’m going to watch the Netflix film adaptation of Stephen King’s Gerald’s game.

Question 2

Addition rule

Answer 2

Pr(A∪B)=Pr(A)+Pr(B)−Pr(A∩B)

Question 3

Mutually exclusive rules

Answer 3

Pr(A∩B)=0

and therefore Pr(A∪B)=Pr(A)+Pr(B)

Question 4

Multiplication rule

Answer 4

Pr(A∩B)=Pr(A∣B)×Pr(B)

Question 5

Law of total probability

Answer 5

Pr(A)=Pr(A∣B)Pr(B)+Pr(A∣B′)Pr(B′)

Question 6

Independent event rules

Answer 6

Pr(A∣B)=Pr(A)
Pr(B∣A)=Pr(B)
Pr(A∩B)=Pr(A)×Pr(B)

Question 7

Expected value of aX+b

Answer 7

E(aX+b)=aE(X)+b

Question 8

Variance of aX+b

Answer 8

Var(aX+b)=a2Var(X)

Question 9

95% rule

Answer 9

Pr(μ−2σ≤X≤μ+2σ)≈0.95

Question 10

Variance

Answer 10

Var(X)=E(X2)−[E(X)]2

Question 11

Standard deviation

Answer 11

σ=sd(X)= root(varX)

Question 12

Binomial distribution yellow box

Answer 12

Photo in favourites.

2 and a half weeks left of year 12… weird.

Question 13

Expected value and variance of binomial

Answer 13

E(X)=np

Var(X)=np(1−p)

Question 14

Rule for continuous

Answer 14

The pdf must equal 1 when anti diffed for the given domain

Question 15

Expected value and median of continuous

Answer 15

E(x) = antidiff x*f(x)

Median solver for antidiff (0 to m) =.5

Question 16

Expected value of G(x) such as xsquared

Answer 16

Antidiff G(x) * F(x)

Question 17

75th percentile

Answer 17

solve continuous like a median but instead the max value is 0.75

Question 18

Interquartile range

Answer 18

The interquartile range is the range of the middle 50%
of the distribution; it is the difference between the 75
th percentile (also known as Q3
) and the 25
th percentile (also known as Q1
).

Question 19

68-95-99.7 Rule

Answer 19

68% of the values lie within one standard deviation of the mean

95% of the values lie within two standard deviations of the mean

99.7% of the values lie within three standard deviations of the mean.

Question 20

Standardised values

Answer 20

standardised value= (data value−mean of the normal curve)/(standard deviation of the normal curve)

z=(x-u)/o

Question 21

Population proportion

Answer 21

p = Number of population with attribute/population size

Question 22

Sample proportion

Answer 22

p̂ = number in sample with attribute/sample size

Question 23

A bag contains six blue balls and four red balls. If we take a random sample of size 4
, what is the probability that there is one blue ball in the sample (p̂ =1/4)?

Answer 23

(NCR(4,3) * NCR (6,1))/NCR(10,4)

NCR(4,3) ways to select 4
balls from 10 balls.

NCR (6,1) ways of choosing one blue ball from 6 blue balls.

NCR(10,4) ways to select 4 balls from 10
balls.

Question 24

Expected value and variance form a large population

Answer 24

Expected value of P̂ is p

Standard deviation of P̂ is root((p(1-p))/n)

where p is the population proportion

Question 25

What probability distribution do you use when sampling from a large population

Answer 25

Binomial distribution

Question 26

Margin of error

Answer 26

The distance between the sample estimate and the endpoints of the confidence interval is called the margin of error (M
) and, for a 95%
confidence interval,

M=1.96 * Root((p̂ (1−p̂))/n)