Truncated Binomial Distribution at X=0

Truncated Binomial at x =0

Meaning of Truncation The literal meaning of truncation is to ‘shorten’ or ‘cut-off’ or ‘discard’ something. We can define the truncation of a distribution as a process which results in certain values being ‘cut-off,’ thereby resulting in a ‘shortened’ distribution. Truncated Distributions Let $X$ be a random variable with pmf/pdf $f(x)$ with distribution function $F(x)$ …

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Truncated Poisson Distribution at X=0

Truncated Poisson at x = 0

Truncated Poisson Distribution (at $X=0$) A discrete random variable $X$ is said to have truncated Poisson distribution (at $X=0$) if its probability mass function is given by $$ \begin{equation*} P(X=x)= \left\{ \begin{array}{ll} \frac{e^{-\lambda}\lambda^x}{(1-e^{-\lambda})x!}, & \hbox{$x=1,2, \ldots$;} \\ & \hbox{$\lambda>0$}\\ 0, & \hbox{Otherwise.} \end{array} \right. \end{equation*} $$ Proof The probability mass function of Poisson distribution $P(\lambda)$ …

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