Binomial and Normal Distribution properties Flashcards
Binomial random variable
A random process with just two possible outcomes. One outcome is arbitrarily labelled success and the other a failure.
Examples:
- Coin toss
- Pass-or-fail test
Bernoulli trial properties
- The result of each trial is either a success or a failure.
- The probability p of a success is the same in every trial.
- The trials are independent; ie, the outcome of each trial has no influence on later outcomes.
Bernoulli random variable
X is the number of success in n Bernoulli trails with probability p of success.
Mean and variance of a binomial distribution
- µ= np*
- σ2 = np(1-p)*
Parameters of a binomial distribution
n and p
where n is the number of trials and p is the probability of success.
Relationship between binomial distribution and the standard normal distribution
The binomial distribution is closely approximatedy by the standard normal distribution when p=0.5 and n is very large.
Steps for transforming a binomial distribution into a standard normal distribution
- Set p to be 0.5
- Make n tend towards infinity.
- Set the mean to be 0 by a linear transformation (ie making it symmetrical about the y axis.
- Set the highest y value such that the area under the curve is 0.