• .examples about 
   distribution function 
  • (binomial- Poisson- exponential- normal ) 
         Binomial 
  Example 1
  If the probability that airplane will hit a target is 
  0.8, than we know five more airplane will hit the 
  target to find the following 
  1) The distribution for all airplane will hit the 
   target?
  2) The mean distribution and its variance?
    Answer 
    n=5, p=0.8, q=1-0.8=0.2 
    Suppose x is the number of airplanes will hit 
    the target, then its x is the binomial density 
    function, is 
            5     x    5 x
    f(x)=  (0.8) (0.2)   ; x 0,1,2,......,5
             
             x
            np5(0.8)4
          2 npq5(0.8)(0.2)0.8
            0.8
     Example2 
     Find the probability of having five heads and seven tails in 12 
     flips of balanced coin?
     Answer 
     X=5, n=12,  p=1\2 
     b(5,12,1\2)=
                        12            x              12 5
                             (1\ 2) (1 1\ 2)
                        5 
                             
                                          12
                        792(1\2) 0.19
                            12                   7              12 7
                                   (1\ 2) (1\ 2)
     b(7,12,1\2)=           7 
                                   
     Complete ……
   Example3 
   • If x is a binomial distribution with parameter 
     p=.1 and n=20, find p(x=3). by using binomial 
     distribution with Poisson distribution?
   • answer
   • *Binomial
    
   • P(x=3)=  20        3      17
                  (.1) (.9)       .19
             3 
                  