A level stats

What do you need for a binomial distribution

2 options

Fixed sample size

Independent, fixed probability

Var/E of a binomial distribution

npq and np

How to standardise the normal distribution

If P(X

Features of a normal distribution

Symmetrical about mean

Mean median and mode all equal

When can we approximate a binomial to a normal

Np>5, nq>5

Mean and var of a sample

Mean and var/n

How to structure conc

There is no evidence at x significance level that (mention context)

Hypothesis testing for 0 correlation

Null hypothesis always 0 correlation

variable is rho - define this

CV = ...

Value calculated >or< CV - reject or fail to reject H0

Specify positive/negative correlation in conclusion relating to H1

How to calculate expected value/mean

Sum of xp

How to work out variance

E(X^2) - (E(x))^2

E(ax+b)

aE(x)+b

Var(ax+b)

a^2Varx

Univorm discrete distribution

Distribution up to n where each value is equally likely (p=1/n)

E(x) for discrete

(N+1)/2

Var(x) for discrete

(N+1)(n-1)/12

Geometric distribution use case

Each trial has exactly 2 possible outcomes

The trials are independent

The probability of success is constant at each trial

Trials continue until success

E(x) for geometric

1/p

Var for geometric

Q/p^2

What is lambda for a poison distribution

Average number of events in the period of interest

Use case of poison distribution

Events occur randomly

Events are independent

Average rate is constant

E(x) for poisson

Lambda

Var(x) for Poisson distribution

Lambda

How to scale Poisson distribution

If no events in an hour is lambda

No events in 2 hours is 2 lambda

How to add Poisson distributions

Z=X+Y

X~Po(lambda)

Y~Po(mu)

Z~Po(lambda + mu)

How many values lie within 1, 2 and 3 standard deviations for normal curve

68% in one

95% in two

99.7% in three

Where are the points of inflection on a nomral curve

mean +- one standard deviation

What to do with minus signs in standard normal

Nothing - leave those ****ers

Expected value of a discrete uniform distribution

(n+1)/2

Var of a discrete uniform distribution

(n+1)(n-1)/12

What is binomial notation

Number of trials, prob of success

What's an assumption for sample testing

Standard deviation stays the same

What are the two definitions of outliers

1.5 IQRs from Q1 or Q3

2 standard deviations from mean

Hypothesis test with p value

Define p

Define another var v

Say result on H0

In conclusion talk abt positive or negative

Difference between spearman and pmcc

Pmcc requires data to be normally distributed

Tests for linear relationship

Spearman's doesn't

And tests for 8ncreasing or decreasing relationship

When to use rank sum vs signed-rank

Signed rank from paired data

Rank-sum from data that is independent and samples can be of different sizes