Probability Flashcards
Memorise probability chapter summaries (This isn’t even necessary anymore, I just originally couldn’t even be bothered to make proper flashcards for prob.)
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.
Addition rule
Pr(A∪B)=Pr(A)+Pr(B)−Pr(A∩B)
Mutually exclusive rules
Pr(A∩B)=0
and therefore Pr(A∪B)=Pr(A)+Pr(B)
Multiplication rule
Pr(A∩B)=Pr(A∣B)×Pr(B)
Law of total probability
Pr(A)=Pr(A∣B)Pr(B)+Pr(A∣B′)Pr(B′)
Independent event rules
Pr(A∣B)=Pr(A)
Pr(B∣A)=Pr(B)
Pr(A∩B)=Pr(A)×Pr(B)
Expected value of aX+b
E(aX+b)=aE(X)+b
Variance of aX+b
Var(aX+b)=a2Var(X)
95% rule
Pr(μ−2σ≤X≤μ+2σ)≈0.95
Variance
Var(X)=E(X2)−[E(X)]2
Standard deviation
σ=sd(X)= root(varX)
Binomial distribution yellow box
Photo in favourites.
2 and a half weeks left of year 12… weird.
Expected value and variance of binomial
E(X)=np
Var(X)=np(1−p)
Rule for continuous
The pdf must equal 1 when anti diffed for the given domain
Expected value and median of continuous
E(x) = antidiff x*f(x)
Median solver for antidiff (0 to m) =.5
Expected value of G(x) such as xsquared
Antidiff G(x) * F(x)
75th percentile
solve continuous like a median but instead the max value is 0.75
Interquartile range
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
).
68-95-99.7 Rule
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.
Standardised values
standardised value= (data value−mean of the normal curve)/(standard deviation of the normal curve)
z=(x-u)/o
Population proportion
p = Number of population with attribute/population size
Sample proportion
p̂ = number in sample with attribute/sample size
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)?
(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.
Expected value and variance form a large population
Expected value of P̂ is p
Standard deviation of P̂ is root((p(1-p))/n)
where p is the population proportion
What probability distribution do you use when sampling from a large population
Binomial distribution
Margin of error
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)