Binomial and Poisson’s distribution using R Studio

Method Name	Documentation
Binomial and Poisson’s distribution using R Studio	Computes the PMF for the binomial distribution.
Binomial and Poisson’s distribution using R Studio	Computes the CDF for the binomial distribution.
Binomial and Poisson’s distribution using R Studio	Computes the quantile function for the binomial distribution.
Binomial and Poisson’s distribution using R Studio	Computes the PMF for the Poisson distribution.
Binomial and Poisson’s distribution using R Studio	Computes the CDF for the Poisson distribution.
Binomial and Poisson’s distribution using R Studio	Computes the quantile function for the Poisson distribution.

R Function Documentation

dbinom()

Description: Computes the probability mass function (PMF) for the binomial distribution.

Usage:

dbinom(x, size, prob, log = FALSE)

Arguments:

• x (integer): Number of successes.
• size (integer): Total number of trials.
• prob (numeric): Probability of success per trial.
• log (logical, default = FALSE): If TRUE, returns the log probability.

Example:

dbinom(48, 51, 0.5)

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pbinom()

Description: Computes the cumulative distribution function (CDF) for the binomial distribution.

Usage:

pbinom(q, size, prob, lower.tail = TRUE, log.p = FALSE)

Arguments:

• q (integer): Number of successes.
• size (integer): Total number of trials.
• prob (numeric): Probability of success per trial.
• lower.tail (logical, default = TRUE): If TRUE, returns P(X ≤ q); if FALSE, returns P(X > q).
• log.p (logical, default = FALSE): If TRUE, returns the log probability.

Example:

pbinom(40, 51, 0.5)

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qbinom()

Description: Computes the quantile function (inverse CDF) for the binomial distribution.

Usage:

qbinom(p, size, prob, lower.tail = TRUE, log.p = FALSE)

Arguments:

• p (numeric): Cumulative probability.
• size (integer): Total number of trials.
• prob (numeric): Probability of success per trial.
• lower.tail (logical, default = TRUE): If TRUE, returns smallest x such that P(X ≤ x) ≥ p.
• log.p (logical, default = FALSE): If TRUE, returns log probability.

Example:

qbinom(0.25, 51, 0.5)

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dpois()

Description: Computes the probability mass function (PMF) for the Poisson distribution.

Usage:

dpois(x, lambda, log = FALSE)

Example:

dpois(3, 7.6)

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ppois()

Description: Computes the cumulative distribution function (CDF) for the Poisson distribution.

Usage:

ppois(q, lambda, lower.tail = TRUE, log.p = FALSE)

Example:

ppois(3, 7.6)

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qpois()

Description: Computes the quantile function for the Poisson distribution.

Usage:

qpois(p, lambda, lower.tail = TRUE, log.p = FALSE)

Example:

qpois(0.25, 7.6)

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References

Information

• date: 2025.02.18
• time: 16:07