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Probability.md

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Probability

MAXIM can compute the distributions of discrete and continuous random variables as described below. Use Ctrl-F to find the function you want quickly.

Binomial Cumulative Distribution Function

Usage: y=bincdf(n,p)

Input: n a non-negative integer; 0 <= p <= 1.

Output: y(i) = P(X <= i-1), i=1,2,...,n+1, where X is a Binomial(n,p) rv.

Binomial Probability Mass Function

Usage: y=binpmf(n,p)

Input: n: a non-negative integer; 0 <= p <= 1.

Output: y(i) = P(X = i-1), i=1,...n+1, where X is a Binomial(n,p) rv.

Erlang Cumulative Distribution Function

Usage: y=erlangcdf(k,l,x)

Input: k >= 1, integer; l >= 0, x is a row vector.

Output: y(i) = F(x(i)), where F is an Erlang(k,l) cdf.

Plot of Erlang Cumulative Distribution Function

Usage: erlangcdfplot(k,l,x),

Input: k >= 1, integer; l >= 0; x is a row vector.

Output: Plot of the cdf of Eralng(k,l) (y vs. x).

Eralng Probability Density Function

Usage: y=erlangpdf(k,l,x)

Input: k >= 1, integer; l >= 0, x is a row vector.

Output: y(i) =f(x(i)), where f is an Erlang(k,l) pdf.

Plot of Erlang Probability Density Function

Usage: erlangpdfplot(k,l,x),

Input: k >= 1, integer; l >= 0, x is a row vector.

Output: Plot of the pdf of Eralng(k,l) (y vs. x).

Exponential Cumulative Distribution Function

Usage: y=expcdf(l,x)

Input: l >= 0, x is a non-negative row vector.

Output: y(i) = F(x(i)), where F is an Exp(l) cdf.

Plot of Exponential Cumulative Distribution Function

Usage: expcdfplot(l,x),

Input: l >= 0, x is a row vector.

Output: Plot of the cdf of exp(l) (y vs. x).

Exponential Probability Density Function

Usage: y=exppdf(l,x)

Input: l >= 0 , x is a row vector.

Output: y(i) =f(x(i)), where f is an Exp(l) pdf.

Plot of Exponential Probability Density Function

Usage: exppdfplot(l,x),

Input: l >= 0, x is a row vector.

Output: Plot of the pdf of exp(l) (y vs. x).

Geometric Cumulative Distribution Function

Usage: y=geometriccdf(p,k)

Input: k >= 1, integer; 0 <= p <= 1.

Output: y(i) = P(X <= i), i=1,2,...,k, where X is a Geometric(p) rv.

Geometric Probability Mass Function

Usage: y=geometricpmf(p,k)

Input: k >= 1, integer; 0 <= p <= 1.

Output: y(i) = P(X = i), i=1,...k, where X is a Geometric(p) rv.

Negative Binomial Cumulative Distribution Function

Usage: y=negbincdf(r,p,k)

Input: r,k >= 1, integer; 0 <= p <= 1.

Output: y(i) = P(X <= i), i=r,r+1,...,r+k, where X is a Negative Binomial(r,p) rv.

Negative Binomial Probability Mass Function

Usage: y=negbinpmf(r,p,k)

Input: r,k >= 1, integer; 0 <= p <= 1.

Output: y(i) = P(X = i), i=r,r+1,...,r+k, where X is a Negative Binomial(r,p) rv.

Normal Cumulative Distribution Function

Usage: y=normalcdf(m,s,x)

Input: s >= 0, x is a row vector.

Output: y(i) = F(x(i)), where F is an Normal(m,s) cdf, with mean m and variance s.

Plot of Normal Cumulative Distribution Function

Usage: normalcdfplot(m,s,x)

Input: s >= 0, x is a row vector.

Output: Plot of the cdf of Normal(m,s) (y vs. x).

Normal Probability Density Function

Usage: y=normalpdf(m,s,x)

Input: s >= 0 , x is a row vector.

Output: y(i) =f(x(i)), where f is an Normal(m,s) pdf, with mean m and variance s.

Plot of Normal Probability Density Function

Usage: normalpdfplot(m,s,x)

Input: s >= 0, x is a row vector

Output: Plot of the pdf of Normal(m,s) (y vs. x).

Poisson Cumulative Distribution Function

Usage: y=poissoncdf(l,k)

Input: 0 <= l <= 700.

Output: y(i) = P(X <= i-1), i=1,2,...,k+1, where X is a Poisson(l) rv.

Poisson Probability Mass Function

Usage: y=poissonpmf(l,k)

Input: 0 <= l <= 700.

Output: y(i) = P(X = i-1), i=1,...k+1, where X is a Poisson(l) rv.