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research methods and data analysis > binominal distribution > Flashcards

binominal distribution Flashcards

1
Q

what is binomial distribution?

A
  • distributions that counts the number of successes in a series of independent trials
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2
Q

what is probability used for?

A
  • used to quantify how likely a set of data was obtained by pure chance
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3
Q

what does probability represent?

A
  • varying degrees of uncertainty
  • how certain we are about the truth of some situation or the cause of outcome
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4
Q

what is n?

A
  • number of trials
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5
Q

what is p?

A
  • probability of success
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6
Q

state the 4 properties of binomial distribution

A
  • a fixed n, the p remains constant, the trial has two possible outcomes (success and failure), trials must be independent
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7
Q

what is the simplest possible data science?

A
  • statistics of coin tossing
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8
Q

what is the probability of getting heads/ tails assumed to be?

A
  • 0.5
  • 50%
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9
Q

what do you do to intuitive statistics?

A
  • 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
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10
Q

what is the equation for probability?

A

Bi (k/n, q)

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11
Q

what does probability ( A/B ) refer to?

A
  • probability of obtaining A on the condition of B
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12
Q

what is probability (A/B) considered as?

A
  • considered as a function that returns a value between 0 and 1 for given parameters k, n and q
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13
Q

what can you do with the equation of probability?

A
  • can mathematically derive an equal calculating Bi (k/n, q)
  • but there is an intuitive way to understand how such function looks like
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14
Q

what can you count?

A
  • how many possible combinations of coins you get k heads out of n tosses
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15
Q

what can you describe the results of tossing a coin 10 time as? what can you find?

A
  • sequence of heads (H) and tails (T)
  • among all possible cases, you will sometimes get a sequence that has k= 3 heads
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16
Q

how do you work out probability of coin tosses?

A

Bi (k/ n, q) = number of sequences with k- heads/ number of all possible sequences

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17
Q

why would you not count number of sequences?

A
  • too tedious and time consuming
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18
Q

what does a decision tree visualise?

A
  • multiple coin toss can be visualised as a connection of branches
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19
Q

what happens at each branch of a decision tree

A
  • you decide whether to go down, left or right based on a coin toss
20
Q

how is N coin toss visualised?

A
  • visualised as a decision tree with n- layers after top node
21
Q

what is Pascal’s triangle decision tree?

A
  • simple binominal distributions computed analytically
22
Q

how do you analyse complicated distributions?

A
  • need to be looked up in binomial table
23
Q

what happens at each node?

A
  • all routes to node from the top have the same number of heads/ tails
24
Q

what do you do as you go down the nodes?

A
  • don’t need to count them all
  • just write down numbers on each node as you go
25
Q

what is the rule relating to the nodes?

A
  • add two number written on nodes in upper later that are connected to you
26
Q

what is the total number of possible sequences?

A
  • sum of all numbers in the same layer
  • number written in each node will be the number of sequences for the corresponding k
27
Q

how do you work out how likely that event happens by chance?

A
  • looking at the binomial distribution for given n and k
28
Q

what does lower probability show?

A
  • higher likelihood of it happening
29
Q

what is cumulative probability?

A
  • probability of getting up to a certain number of successes
30
Q

what happens to cumulative probability when the number of coin tosses becomes high?

A
  • 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
31
Q

what is a two- tailed probability?

A
  • taking the cumulative probability at both ends to check the probability that a data is deviated from the centre
32
Q

is binominal distribution limited to coin toss?

A
  • no, not limited to q being 0.5
  • can be 0 < q< 1
33
Q

what is coin tossing described as? and why?

A
  • discrete
  • you can count how many times something happened
34
Q

is binomial distribution discrete?

A
  • it is discrete distribution as distribution is a bunch of numbers located at each count
35
Q

what are discrete events used for?

A
  • used for countable events
36
Q

what are examples of continuous variables?

A
  • height
  • weight
  • error
37
Q

what distribution do you need when measuring continuous variables ?

A
  • need continuous distribution to describe a distribution of a continuous variable
38
Q

what is the probability of a variable being a specific number in continuous distribution?

A
  • probability is zero
    e.g., what is the probability of someone’s weight being exactly 60.0000kg
39
Q

what do we need for the probability of continuous variables?

A
  • need it in a certain range like cumulative distribution
    e.g., what is the probability that someone weighs 50-60kg
40
Q

what indicates probability on a graph?

A
  • area under the distribution in that range
41
Q

what is probability density?

A
  • Y- axis of continuous distribution is not the probability
42
Q

what number is the area under whole continuous distribution?

A
  • always 1
43
Q

what is normal distribution?

A
  • continuous distribution
  • conveniently described by two numbers including the mean and SD
44
Q

what happens as number of tosses increases?

A
  • specific shape becomes clearer
  • increased symmetry and normal distribution
45
Q

why is normal distribution important?

A
  • most important distribution as describes many natural phenomena and forms bases for various statistical methods

research methods and data analysis (10 decks)

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