Level 3 stats distributions

What does Poisson distribution give us

the probability of a certain number occurring

What are the Poisson distributions conditions?

RIPS

what does the R stand for in RIPS

random occurrence at a constant rate

what does the I stand for in RIPS

Independence of occurrences

what does the P stand for in RIPS

Probability of occurring is proportional

what does the S stand for in RIPS

simultaneous events are impossible

what is PPD and BPD used for

the exact number

what is PCD and BCD used for

a group of numbers eg more than or less than

P(x≤4)

up to 4

P(x≤3)

less than 4

1- P(x≤4)

more than 4

1- P(x≤3)

at least 4

P(x≤4) - P(x≤1)

between 2 and 4

what is x

number of occurrences

what is λ

average rate of occurrences

what is in this image

the inverse poisson formula

what distributions are continuous

Triangular, Uniform, Normal

what distributions are discrete

binomial, poisson

Triangular Distribution

the distribution has a maximum and a minimum x-vaule and the highest point is the mode

height at x on left of mode

2(x-a)/(b-a)(c-a)

height at x on right of mode

2(b-x)/(b-a)(b-c)

height at mode

2/b-a

how do we justify triangular distribution

there is a maximum and minimum x-value

we have the mode

the distribution is continuous

the distribution is often skewed to one side

for uniform distribution every x-value has the same height...

same probability of occurring

justify uniform distribution

there is a maximum and minimum x-value

all possible x-values have the same probability of occurring

the distributions is continuous

for normal distribution use...

NCD

justify normal distribution

the mean median mode are in the middle

almost all values are within 3 S.D of the mean

the distribution is symmetrical

there is no maximum or minimum x-value

continuous variables are.... and rounding makes the variable....

mesurable, discrete

when to use binomial distribution

discrete variable

two possible outcomes

fixed number of trials

When to use poisson distribution

discrete variable

rate of occurrence

no upper limit on number

When to use normal distribution

continuous variable

central mean median mode

symmetrical bell curve

uses standard deviation

when to use Triangular distribution:

continuous variable

maximum and minimum

clear mode

When to use uniform distribution

continuous variable

maximum and minimum

same probability for all x

comes from counting the number of successes in a fixed set of trials

binomial distribution

what are the binomial conditions?

PITT

what does the P in PITT stand for

probability of success is fixed

what does the I in PITT stand for

independence of trials

what does the first T in PITT stand for

two possible outcomes of trials

what does the second T in PITT stand for

trial number is fixed

if events are independent

P(AnB) = P(A) x P(B)

calculating conditional probability

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

probability of someone having a dog knowing they have a cat is

P(dog|cat) = P(dog n cat)/P(cat)

what is this image

inverse binomial problems