M89 - Binomial Random Variable

• The Binomial Experiment Conditions

  • The experiment consists of n identical independent trials
  • Each trial results in one or two outcomes (Success/Failure)
  • The probability of success on a single trial is p and remains constant from trial to trial. The Probability of failure is q = 1-p
  • The trials are independent.
  • We are interested in x, the number of success in n trials
• Binomial experiment formula:

  n = number of trials

  p = probability of success on a given trial

  q = probability of failure

  k = probability of successes in n trial 


  
  

  
  

  $P(x=k) =$$C^n_k p^kq^{n-k} =$$\frac{n!}{k!(n-k)!}p^kq^{n-k}$

  for k = 0,1,2,..n.

  q = 1 - p
• Mean formula for a binomial experiment

  where n = # of trials

  p = probability p of success on a given trial

  $\mu =$$np$
• Variance formula for a binomial experiment

  $\sigma^2 =$$npq$

  where n = # of trials

  p = probability of success on a given trial

  q = 1 - p (probability of failure)
• Standard Deviation formula for a binomial experiment 


  $\sigma =$$\sqrt{npq}$
• You can use the cumulative probability tables to find probabilities for selected binomial distributions.
• Steps for using Cumulative Probability Tables

  1)Find the table for the correct value of n.

  2)Find the column for the correct value of p.

  3)The row marked “k” gives the cumulative probability, P(x<= k) = P(x = 0) +…+ P(x = k)