CH.4 - BINOMIAL DISTRIBUTION

CH.4 - BINOMIAL DISTRIBUTION

1. BERNOULLI DISTRIBUTION

   • Consider a random experiment giving rise to two mutually exclusive and collectively exhaustive outcomes
     • i.e outcomes are success and failure
     • P denotes prob. of success
       • 1-P is prob. of failure
         • Probability distribution is then P(0)=(1-p) and P(1)=P
           • This is known as Bernoulli distribution
           • MEAN AND VARIANCE BERNOULLI RANDOM VARIABLE
             • MEAN:
             • VARIANCE:

2. DEVELOPING THE BINOMIAL DISTRIBUTION

   • Number of sequences with x successes in n trials
   • THE BINOMIAL DISTRIBUTION
     • Suppose that a random experiment can result in two mutually exclusive and collectively exhaustive outcomes, success and failure.
     • if n independant trials are carrried out, the distribution of the resulting number of successes, x, is called the binomial distribution
   • MEAN AND VARIANCE OF A BINOMIAL PROBABILITY DISTRIBUTION
     • Let x be the number of successes in n independant trials, each with success probability P. Then X follows a probability distribution with mean and variane