Changes

  Each trial represents only two results(Success or failure)

  Each trial represents only two results(Success or failure)

  The probability of success is constant from trial to trial

  The probability of success is constant from trial to trial

  The trials are independent; that is, 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 r successes are observed, where r 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  x = the number of failures that precede the rth success;  

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

*x 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.

*Then  probability mass function of the negative binomial distribution is:

*Then  probability mass function of the negative binomial distribution is:

nb(x;r,p)=(x+r-1 p^r (1-p)^x  r-1)         

nb(x;r,p)=(x+r-1 p^r (1-p)^x  r-1)         

*For example:If a fair coin is tossed repeatedly, what is the probability that at least 10 tosses are required.

*For example: If a fair coin is tossed repeatedly, what is the probability that at least 10 tosses are required.

to obtain heads 8 times

to obtain heads 8 times

*This function will give the result as error when:

*This function will give the result as error when: