sons dataStory

Content Contents Geometric distribution Negative Binomial Distribution Hypergeometric distribution Poisson distribution Discrete probability distribution II : Geometric, Negative Binomial, Hypermatric, and Possion Geometric distribution The distribution of probability change until the first success after repeating Bernoulli trials is called geometric distribution . For example, the probability mass function with the random variable X being the first success(s) by repeating Bernoulli trials with a probability of success p will be as follows. $$\begin{align}&R_x=\{1,\, 2,\, \cdots \}\\&f(1)=P(X=1)=p\\ &f(2)=P(X=2)=(1-p)p \\& \qquad \vdots\end{align}$$ Generalizing the above results, the probability mass function of the geometric distribution can be formulated as Equation 1. $$\begin{equation}\tag{1} f(x)=P(X=x)=(1-p)^{x-1}p\\ \end{equation}$$ As in Equation 1, the probability mass function depends only on the parameter p. Therefore, it is called a...