Week 2 Probability Distributions

Question 1

define intersection and union

Answer 1

intersection is where both variables need to be true to return true
union is where at least one of the variables must return true to be true

Question 2

what is Bayes theorem

Answer 2

conditional probability of an event A given an event B is defined as the ratio of the probability of the intersection of A and B and the probability of event B

Question 3

what is the Bayes theorem equation in axiom terms

Answer 3

P( A I B ) = P(A∩B) / P(B)

Question 4

what is the Bayes theorem equation in condensed terms

Answer 4

P = I L / E
P is the posterior probability
I is the prior probability
L is the likelihood probability
E is the evidence

Question 5

what is the probability mass function

Answer 5

probability distribution used when a result can only take a limited number of values

Question 6

what is the probability density function

Answer 6

probability distribution used when a result is continuous

Question 7

what does the Binomial distribution do

Answer 7

describes processes with a given number of identical trials with two possible outcomes.

Question 8

what is the Binomial distribution equation

Answer 8

P(k; n,p) = p^k (1-p)^(n-k) n!/k!(n-k)!
k is the number of successes
n is the number of trials
p is the probability of an individual success

Question 9

what does the Poisson distribution do

Answer 9

describe processes in which the probability of a certain number of event occurring in a given interval of time

Question 10

what are the two pre conditions for the Poisson distribution

Answer 10

the average occurrence rate of event is a known constant and the events are independent of each other

Question 11

what is the Poisson distribution equation

Answer 11

P(k;λ) = e^-λ λ^k / k!
k is the number of times an event occurs
λ is the average event rate

Question 12

what is the Gaussian distribution

Answer 12

a continuous and symmetric probability distribution

Question 13

what is the Gaussian distribution equation

Answer 13

P(x; μ,σ) ~ N(μ,σ^2) = 1 / σsqrt[2π] e^-[(x-μ)^2 / 2σ^2]
σ is the standard deviation
μ is the mean of the Gaussian

Question 14

what happens to binomial and poisson distributions when n and λ are infinity

Answer 14

they become Gaussian distributions

Question 15

what are the 5 other probability distributions

Answer 15

Uniform
Chi Squared
Student's t distribution
F-distribution
Multivariate distribution

Question 16

define a uniform probability distribution

Answer 16

distribution where all values in an interval have equal values

Question 17

define the chi squared probability distribution

Answer 17

distribution of a sum of the squares of k independent standard normal random variables

Question 18

define the student’s t distribution probability distribution

Answer 18

frequency distribution of standard deviations of samples drawn from a normal distribution

Question 19

define the F distribution probability distribution

Answer 19

distribution used when comparing statistical models that have been filled to a dataset in order to identify the model best suited

Question 20

define the multivariate gaussian probability distribution

Answer 20

generalisation of 1 dimension normal distributions to higher dimensions