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Presentation at the Course ‘Biostatistics MSN823’, Level 2 Year 1, Faculty of Nursing, Princess Noura bint Abdulrahman University. By Prof. Omar Hasan Kasule Sr. MB ChB (MUK), MPH (Harvard) DrPH (Harvard)
Variable Distributions
- Discrete distributions
- Continuous distributions
Discrete Probability
Distributions - Bernoulli
- Bernoulli (a single trial with only two outcomes with probabilities p and 1-p. Bernoulli is a special case of the binomial with only one trial.
- The graph of a Bernoulli distribution helps to get a visual understanding of the probability density function of the Bernoulli random variable.
Figure: Plot of the Bernoulli Distribution
Discrete Probability
Distributions - Binomial
- Binomial a fixed number of independent trials with probability of success fixed and the same for each trial, each trial has a binary outcome i.e. yes/no, the binomial distribution is the number of successes.
- Binomial is essentially Bernoulli with repetition.
Figure: Plot of the Binomial
Distribution
Discrete Probability
Distributions-Multinomial, Geometric, Hypergeometric, Poisson
- Multinomial, like binomial, but more than 2 outcomes.
- Geometric is the same as binomial, but the number of trials is not fixed.
- Hypergeometric is sampling from a finite population without replacement.
- Poisson is the occurrence of an event over an interval of time or space and approximates the binomial with large n. Poisson is used to determine the probability of rare events.
FIGURE: Multinomial
Distribution
FIGURE GEOMETRIC DISTRIBUTION
FIGURE HYPEGEOMETRIC
DISTRIBUTION
FIGURE: POISSON DISTRIBUTION
FORMULAS OF DISCRETE DISTRIBUTIONS
Each of the distributions can be
represented by a complicated formula that enables us to compute a theoretical
probability (we do not have to carry out the trials, but the calculated answer
will equal the answer from repeated empirical trials). Each formula has
specific parameters: Binomial (n and P), Poisson ( l).