Manuals/calci/BERNOULLIDISTRIBUTED

BERNOULLIDISTRIBUTED (Numbers,Probability)

• $Numbers$ is the number of variables.
• $Probability$ is the value range from 0 to 1.

Description

• This function gives the value of the Bernoulli distribution.
• It is a discrete probability distribution.
• Bernoulli distribution is the theoretical distribution of the number of successes in a finite set of independent trials with a constant probability of success.
• The Bernoulli distribution is simply BINOM(1,P).
• This distribution best describes all situations where a trial is made resulting in either success or failure, such as when tossing a coin, or when modeling the success or failure.
• In $BERNOULLIDISTRIBUTED(Numbers,Probability)$ ,$Numbers$ represents the number of variables.
• $Probability$ is the probability value.
• The $Probability$ vaule is ranges from 0 to 1.
• The Bernoulli distribution is defined by:Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x)=p^x(1-p)^{1-x} } for x={0,1}, where p is the probability that a particular event will occur.
• The probability mass function is :

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(k,p) = \begin{cases} p if & k=1\\ (1-p) if & k=0. \\ \end{cases}}

• This function will give the result as error when

1. Any one of the argument is non numeric.
2. The value of p<0 or p>1.

\begin{cases} 3x + 5y + z &= 1 \\ 7x - 2y + 4z &= 2 \\ -6x + 3y + 2z &= 3 \end{cases}