Probability Distribution Function of Discrete Distribution
I. Discrete Uniform Distribution
The Discrete Uniform Distribution represents outcomes where each possible value has an equal chance of occurring. For example, rolling a fair six-sided die is a classic case of discrete uniform distribution.
The Bernoulli Distribution is applicable to situations with two possible outcomes, typically labeled as success and failure. It is often used in scenarios like coin flips, where success might be getting heads.
P(X = x) = px (1-p)1-x, x = 0, 1; 0 < p < 1
Binomial Distribution deals with the number of successes in a fixed number of independent Bernoulli trials. For instance, determining the probability of getting a certain number of heads in multiple coin flips.
P(X = x) = nCx px (q)n-x, x = 0, 1, 2,……,n; 0 < p < 1
IV. Geometric Distribution
Geometric Distribution models the number of trials needed for the first success in a sequence of independent Bernoulli trials. For example, finding the probability of the first successful free throw in basketball.
P(X = x) = (1 – p)k-1.p
The Negative Binomial Distribution focuses on the number of trials needed for a fixed number of successes in a sequence of independent Bernoulli trials. It’s applicable to scenarios like predicting the number of attempts to make three successful shots in basketball.
The Poisson Distribution is useful for events with a known average rate of occurrence within a fixed interval. It’s commonly employed in areas, such as predicting the number of emails received in an hour.
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