Changes

  The trials are independent; ie, the outcome on one trial does not affect the outcome on other trials.

  The trials are independent; ie, the outcome on one trial does not affect the outcome on other trials.

  The experiment continues until <math>r</math> successes are observed, where <math>r</math> is a specified positive integer.  

  The experiment continues until <math>r</math> successes are observed, where <math>r</math> is a specified positive integer.  

*The random variable of  <math>x</math> = the number of failures that precede the <math>r^th</math> success;  

*The random variable of  <math>x</math> = the number of failures that precede the <math>r^{th}</math> success;  

*<math>x</math> is called a Negative Binomial Random variable because, in contrast to the  

*<math>x</math> is called a Negative Binomial Random variable because, in contrast to the  

binomial random variable, the number of successes is fixed and the number of trials is random.

binomial random variable, the number of successes is fixed and the number of trials is random.