important points in 7.5.4:

• • understanding discrete vs. continuous
    
    
  • for a continuous random variable, probabilities of an interval of values are represented by areas (that are sectioned off by vertical slices).
    
    
  • for a continuous random variable the probability that x=( any specific value) = 0.  for a continuous variable there are an infinite number of possible values the variable can have.  even if you think of each one as equally likely (as in a uniform distribution), the probability of any one particular value is 1/(infinity) which is 0.
    
    
  • " expected value " is a term that means the mean (average)
    
    
  • the mean (“expected value”) is the "balance point" of the area