Binomial CDF

Notes:

• In the upper limit of the sum given above, we have
  When x is equal to one of the integers 0, 1, ..., n, the above cdf reduces to the cumulative probability
  
  
  For example, when X has a Bin(10,0.5) distribution, the value of the cdf at x = 4 is
  
  This is represented as a shaded area under the Bin(10,0.5) probability histogram in the figure below.
  
• Cumulative binomial probabilities may be found using a table of such probabilities (e.g., see Table 1) or by appropriate computer software.