binominal distribution Flashcards
what is binomial distribution?
- distributions that counts the number of successes in a series of independent trials
what is probability used for?
- used to quantify how likely a set of data was obtained by pure chance
what does probability represent?
- varying degrees of uncertainty
- how certain we are about the truth of some situation or the cause of outcome
what is n?
- number of trials
what is p?
- probability of success
state the 4 properties of binomial distribution
- a fixed n, the p remains constant, the trial has two possible outcomes (success and failure), trials must be independent
what is the simplest possible data science?
- statistics of coin tossing
what is the probability of getting heads/ tails assumed to be?
- 0.5
- 50%
what do you do to intuitive statistics?
- quantify the statistics using binominal distribution
- calculate the probability of getting k heads in n tosses where the probability of getting heads for each toss is q
what is the equation for probability?
Bi (k/n, q)
what does probability ( A/B ) refer to?
- probability of obtaining A on the condition of B
what is probability (A/B) considered as?
- considered as a function that returns a value between 0 and 1 for given parameters k, n and q
what can you do with the equation of probability?
- can mathematically derive an equal calculating Bi (k/n, q)
- but there is an intuitive way to understand how such function looks like
what can you count?
- how many possible combinations of coins you get k heads out of n tosses
what can you describe the results of tossing a coin 10 time as? what can you find?
- sequence of heads (H) and tails (T)
- among all possible cases, you will sometimes get a sequence that has k= 3 heads
how do you work out probability of coin tosses?
Bi (k/ n, q) = number of sequences with k- heads/ number of all possible sequences
why would you not count number of sequences?
- too tedious and time consuming
what does a decision tree visualise?
- multiple coin toss can be visualised as a connection of branches
what happens at each branch of a decision tree
- you decide whether to go down, left or right based on a coin toss
how is N coin toss visualised?
- visualised as a decision tree with n- layers after top node
what is Pascal’s triangle decision tree?
- simple binominal distributions computed analytically
how do you analyse complicated distributions?
- need to be looked up in binomial table
what happens at each node?
- all routes to node from the top have the same number of heads/ tails
what do you do as you go down the nodes?
- don’t need to count them all
- just write down numbers on each node as you go
what is the rule relating to the nodes?
- add two number written on nodes in upper later that are connected to you
what is the total number of possible sequences?
- sum of all numbers in the same layer
- number written in each node will be the number of sequences for the corresponding k
how do you work out how likely that event happens by chance?
- looking at the binomial distribution for given n and k
what does lower probability show?
- higher likelihood of it happening
what is cumulative probability?
- probability of getting up to a certain number of successes
what happens to cumulative probability when the number of coin tosses becomes high?
- doesn’t make much sense of using the probability of getting the exact number of heads
- makes more sense to use the probability that the value falls in a certain range
what is a two- tailed probability?
- taking the cumulative probability at both ends to check the probability that a data is deviated from the centre
is binominal distribution limited to coin toss?
- no, not limited to q being 0.5
- can be 0 < q< 1
what is coin tossing described as? and why?
- discrete
- you can count how many times something happened
is binomial distribution discrete?
- it is discrete distribution as distribution is a bunch of numbers located at each count
what are discrete events used for?
- used for countable events
what are examples of continuous variables?
- height
- weight
- error
what distribution do you need when measuring continuous variables ?
- need continuous distribution to describe a distribution of a continuous variable
what is the probability of a variable being a specific number in continuous distribution?
- probability is zero
e.g., what is the probability of someone’s weight being exactly 60.0000kg
what do we need for the probability of continuous variables?
- need it in a certain range like cumulative distribution
e.g., what is the probability that someone weighs 50-60kg
what indicates probability on a graph?
- area under the distribution in that range
what is probability density?
- Y- axis of continuous distribution is not the probability
what number is the area under whole continuous distribution?
- always 1
what is normal distribution?
- continuous distribution
- conveniently described by two numbers including the mean and SD
what happens as number of tosses increases?
- specific shape becomes clearer
- increased symmetry and normal distribution
why is normal distribution important?
- most important distribution as describes many natural phenomena and forms bases for various statistical methods
