Stats Final push

Average Expected of random variable

X is a random variable

x is the specific outcome X can take

Average expected for a sample

Variance

Square each x and multiply by their respective probability and sum them. Then minus from the square of the mean.

Standard deviation

Root of variance

Combinations

n = number of sets

x = number of objects

eg picking 2 (x) out of 3 (n) vegetables.

Probability of certain combination

Find the combination for it, then divide by the total number of outcomes.

Binomial distribution function

Binomial distribution layout, mean and variance

X~B(n,P)

Mean: nP

Variance: nP(1-P)

Poisson Distribution function

• myoo = mean

• x = number of sucesses

• remember that successes and mean are proportional

Approximation to binomial

Binomial is nP but when nP is equal or less than 7 we use poisson.

Normal Distribution

• x is a particular value under X the random variable

• eg height of student X x = 170cm

Standardised normal distribution

Using z values

5% ci = 1.96

10% ci = 1.645

1% = 2.576%

Sample X

Hypithesis testing with unknown pop variance and small sample

Use t-test

use sample variance and calculate as usual.

THen use degrees of freedpm (n-1) and the t statstical table to fins t value.