[Solution] An extension of the Geometric distribution that we learned in class is so-called Negative Binomial distribution. Let X be the number of Bernoulli
Question: An extension of the Geometric distribution that we learned in class is so-called Negative Binomial distribution. Let X be the number of Bernoulli trials on which the r th success occurs, then X has a Negative Binomial distribution with parameter r and p (Bernoulli probability of success). The Geometric distribution is a special case when r=1. Read the detail about this distribution on page 241, especially the shaded block including the pmf, the mean and variance. Use these to do Problem 5.41 and 5.43 (b) on page 245. (7)
The pmf on the page 243 has a typo! The correct pmf is as follows:
\[p(y)=\left( \begin{matrix} y-1 \\ r-1 \\ \end{matrix} \right){{p}^{r}}{{(1-p)}^{y-r}},y=r,r+1,...\]
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