Common Distributions

Binomial Distribution

Binomial distribution

Suppose:

• trials - each of which have two possible outcomes
• Each trial has same probability of success
• trials are independent

The total number of successes in trials in a binomial random variable.

Probability of successes:

• Mean of is .
• Variance of is

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Poisson Distribution

Poisson distribution

Random variable follows Poisson distribution with parameter if:

where

• is approximately
• is the expected no. of events per time unit
• is the expected no. of events over time period

A binomial distribution with large , small can be accurately approximated by a Poisson distribution with parameter .

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Normal Distribution

Normal distribution

• symmetric
• bell-shaped
• characterized by mean , variance

Addition of normal variables If

Multiplying a constant to normal variables If

Standardisation of normal variables If

• if -score is or , it is an outlier

Normal Approximation to the Binomial Distribution

If the following conditions are satisfied, tends to be symmetric and is well approximated by a normal distribution .

• is moderately large
• not too close to 0 or 1

Condition for approximation to be good: