Binomial and Normal Distribution properties Flashcards

1
Q

Binomial random variable

A

A random process with just two possible outcomes. One outcome is arbitrarily labelled success and the other a failure.

Examples:

  1. Coin toss
  2. Pass-or-fail test
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2
Q

Bernoulli trial properties

A
  1. The result of each trial is either a success or a failure.
  2. The probability p of a success is the same in every trial.
  3. The trials are independent; ie, the outcome of each trial has no influence on later outcomes.
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3
Q

Bernoulli random variable

A

X is the number of success in n Bernoulli trails with probability p of success.

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4
Q

Mean and variance of a binomial distribution

A
  • µ= np*
  • σ2 = np(1-p)*
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5
Q

Parameters of a binomial distribution

A

n and p

where n is the number of trials and p is the probability of success.

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6
Q

Relationship between binomial distribution and the standard normal distribution

A

The binomial distribution is closely approximatedy by the standard normal distribution when p=0.5 and n is very large.

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7
Q

Steps for transforming a binomial distribution into a standard normal distribution

A
  1. Set p to be 0.5
  2. Make n tend towards infinity.
  3. Set the mean to be 0 by a linear transformation (ie making it symmetrical about the y axis.
  4. Set the highest y value such that the area under the curve is 0.
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