Life expectancy subclass of lifetime
Calculation
In actuarial notation, the probability of surviving from age 
  
    
      
        x
      
    
    {\displaystyle x}
   to age 
  
    
      
        x
        +
        n
      
    
    {\displaystyle x+n}
   is denoted 
  
    
      
        
          
          
            n
          
        
        
          p
          
            x
          
        
        
      
    
    {\displaystyle \,_{n}p_{x}\!}
   and the probability of dying during age 
  
    
      
        x
      
    
    {\displaystyle x}
   (i.e. between ages 
  
    
      
        x
      
    
    {\displaystyle x}
   and 
  
    
      
        x
        +
        1
      
    
    {\displaystyle x+1}
  ) is denoted 
  
    
      
        
          q
          
            x
          
        
        
      
    
    {\displaystyle q_{x}\!}
   . For example, if 10% of a group of people alive at their 90th birthday die before their 91st birthday, the age-specific death probability at 90 would be 10%. This probability describes the likelihood of dying at that age, and is not the rate at which people of that age die. It can be shown that
The curtate future lifetime, denoted 
  
    
      
        K
        (
        x
        )
      
    
    {\displaystyle K(x)}
  , is a discrete random variable representing the remaining lifetime at age 
  
    
      
        x
      
    
    {\displaystyle x}
  , rounded down to whole years. Life expectancy, more technically called the curtate expected lifetime and denoted 
  
    
      
        
        
          e
          
            x
          
        
        
      
    
    {\displaystyle \,e_{x}\!}
   , is the mean of 
  
    
      
        K
        (
        x
        )
      
    
    {\displaystyle K(x)}
  —that is to say, the expected number of whole years of life remaining, assuming survival to age 
  
    
      
        x
      
    
    {\displaystyle x}
  . So,
is a type of is a kind of is a subtype of belongs to category is classified as