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Binomial Distribution

 

Discrete Distribution:

  • Variables can take 2 values (success / failure)
     
  • Expected Value = np
     
  • Variance = np (1-p) (constant)
     
  • Can describe changes in the value of an asset or portfolio    

  



The probability distribution for a Binomial Random Variable is given by:
  • Mean = np
  • Variance = np(1-p)

Sample Question

 

Example

The Prob. of a stock moving up is 0.8 and moving down is 0.2 in a particular day. What is the probability that it would move up at least twice in the 5 working days of the week?

Solution

P = 0.8, q = 0.2, n = 5
P(X >= 2) = 1 - P(X = 0) - P(X = 1)

= 1 - (0.2)5 - 5*(0.8)1*(0.2)4
= 0.99328





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