Usages of those 4 distributions 
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  Case #1:  x_mean = x0,  std is given    ->  Apply a normal distribution 
  Case #2:  x_mean > x0,  std is given    ->  Apply a normal distribution 
  Case #3:  x_mean < x0,  std is given    ->  Apply a normal distribution 

  Case #4:  x_mean = x0,  std is not given    ->  Apply a t-distribution 
  Case #5:  x_mean > x0,  std is not given    ->  Apply a t-distribution 
  Case #6:  x_mean < x0,  std is not given    ->  Apply a t-distribution 
 
  Case #7:  var  = var0,    ->  Apply a Chisq distribution 
  Case #8:  var  > var0,    ->  Apply a Chisq distribution 
  Case #9:  var  < var0,    ->  Apply a Chisq distribution 

  Case #10:  var1  = var2,    ->  Apply a F-distribution 
  Case #11:  var2  > var2,    ->  Apply a F-distribution 
                        var1
           f-statistic = ------
                        var2
           var1>var2
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Explain the concept of 'does their mean equal zero?;             
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  The first set values have a mean of 0.05, while the second one with e 
     mean of 0.01. Which one is close to zero? 
     Many would answer that 0.01 is close to zero               

   However, this is not correct. Let's look at some hypothetical values                                     
   0.012, 0.02,0.01,0.005,0.006,0.012,0.009,0.009,0.001,0.013,0.012,0.011,0.01                                            
                                                                   
   Obviously, the mean of this set is not zero. If we ask 'is the next period return is zero?'                   
   By just looking at those values, we could say NO.            
     
   The second set of values are given below.                   
   0.30, -0.10,-0.135,-0.105,0.35,0.32,-0.10,-0.05,0.25,-0.13,0.21,0.28,0.21                                       
                                                                   
   If we ask 'is the next period return is zero?'
      By just looking at those values, we could not answer.        
     
   Methodology:                                                  
    Step 1: calculate mean                                        
    Step 2: calculate standard deviation            std           
    Step 3: calculate standard error      stdErr = ---------       
                                                    sqrt(n)        
   where std is from step 2, sqrt() is the squared root, n is the number of observations       
    Assume that we choose 5% confidence level                     
    we calculate 95% confidence interval                          
      [mean-2*stdErr,    mean + 2*stdErr]                          
If 0 is in the interval, it means that the mean is not statistically different from zero.                           
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