EDA-Lesson 7

• Mean of the Binomial Distribution


  u = Nn (where N is the number of trials and n is the probability of success on each trial)
• Standard Deviation of the Binomial Distribution

  Positive square root of variance
• A random experiment consists of n Bernoulli trials such that

  • The trials are independent
  • Each trial results in only two possible outcomes, labeled as success and failure
  • The probability of a success in each trial, denoted as p, remains constant.
• Binomial Distribution


  A probability distribution that describes the number of successes in a fixed number of independent Bernoulli trials
• Poisson Process

  • A random experiment with events that occur in an interval and satisfy the following assumptions
  • 
    
  • The interval can be partitioned into subintervals such that the probability of more than one event in a subinterval is zero
  • 
    
  • The probability of an event in a subinterval is proportional to the length of the subinterval
  • 
    
  • The event in each subinterval is independent of other subintervals
• Key Characteristics of the Binomial Distribution

  • Discrete Probability Distribution
  • Bernoulli Trials
  • Independence
  • Fixed Number of Trials
• Variance of the Binomial Distribution

  o^2 = Nn(1-n)