Probability distribution calculator
Which distribution to use
Use the binomial for the number of successes in a fixed number of independent tries, such as heads in 10 coin flips. Use the Poisson for counts of events in a period when they arrive independently at a steady rate. Use the normal for sums and averages of many small independent effects, which is why it appears everywhere.
Rules worth knowing by heart
For a normal distribution, about 68% of outcomes fall within one standard deviation of the mean, 95% within two and 99.7% within three. A binomial with n tries and probability p has mean np and variance np(1 − p). A Poisson has mean and variance both equal to its rate.
Practise it
Frequently Asked Questions
When can I approximate a binomial with a normal?
When both np and n(1 − p) are comfortably above 5. Use mean np and variance np(1 − p).
What range does the probability cover?
From the lower to the upper bound inclusive. For the discrete distributions the bounds are rounded to whole numbers.
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For education and interview practice only. Not investment advice.