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  1. What is the definition of a derivative?
    Limit as delta-x approaches zero of:

    • f(x + delta-x) - f(x) 
    •         delta-x
  2. What is the domain of a function?
    All the values that can be plugged into an equation.
  3. What is the range of a function?
    All the values that can come out of a function.
  4. How do you find the limit of the ratio of 2 functions?
    • derivative of f(x)/ derivative of g(x)
    • do this until you are left with one constant.
  5. When does a function not have a horizontal asymptote?
    If the limit of the function as x goes to positive and negative infinity are both equal to positive and/or negative infinity, then the function does not have horizontal asymptotes.
  6. Where do vertical assymptotes occur?
    Where the function is undefined.
  7. How do you find critical points?
    Take the derivative of the function, set = 0 and solve for all values of x, these are the critical points
  8. How do you find the area under the curve of a function?
    take the integral, plug in b call it F(b), then subtract F(a).
  9. How do you find the area under a curve that goes to infinity?
    Take the limit of the integral as x--> infinity.
  10. Where do inflection points occur?
    Where the second derivative = 0.
  11. What does n stand for in a statistics equation?
    The number of trials that will be performed.
  12. What does k stand for?
    • How many times there is a positive outcome.
    • Or
    • The number of trials until the event has occured.
  13. What does p stand for?
    The probability of a positive outcome.
  14. What does q stand for?
    The probability of the a negative outcome (1-p).
  15. What is the formula of the Geometric Distribution?
    Image Upload 1
  16. What is the probability of a positive result in a single trial in a Geometric Distribution? (math expectation)
  17. What is the math expectation in a Geometric Distribution?
    Image Upload 2
  18. What is the formula of Standard Deviation? (Image Upload 3)
    Image Upload 4
  19. How do you find a density function (f(x)) of a regular function (F(x))?
    The density function is the derivative of the function for each interval.
  20. How do you find the expectation, E(X) of a density function?
    For a continuous random variable.
    Image Upload 5
  21. What is the formula for Variance? Var(X)
    Image Upload 6

    Image Upload 7
  22. What Kind of Distribution is used for a situation where x can take on an infinite number of values?
    Continuous or Normal Distribution.
  23. What are the variable for the binomial equation?
    • p = the probability of a positive outcome
    • q = the probability of a negative outcome
    • n = the number of trials
    • k= how many times there is a positive outcome.
  24. When the question asks how many times will A occur after after n trials, or what is the probability of A occurring after n trials
    • Binomial Distribution:
    • Image Upload 8
  25. When the question asks how many trial until event A occurs, or the probability that an event occurs after a certain number of trials?
    • Geometric distribution:
    • Image Upload 9
  26. The probability of A and B occurring:
    Image Upload 10
  27. The probability of A or B occurring:
    Image Upload 11
  28. What is a discrete variable?
    A variable with a countable number of outcomes
  29. What is a continuous variable?
    A variable with an infinite number of outcomes.
  30. The cumulative distribution notation:
  31. The density function notation:
  32. How do you go from the density function to the continuous random variable?
    Take the integral from - infinity to infinity (usually in three sections)
  33. How do you go from the continuous function to the density function?
    Take the derivative (usually three sections)
  34. When can you not use the binomial distribution?
    When n is very large.
  35. What do you use when n is very large and the probability is >0.1?
    • The Normal approximation:
    • Image Upload 12 etc...
  36. If n is large and p(A) is very small (<0.1) we use:
    • The Poisson distribution.
    • Image Upload 13
  37. The formula for the math expectation:
    Image Upload 14
  38. The sum of the math expectation:
    Image Upload 15
  39. The product of the math expectation:
    Image Upload 16
  40. The formula of the math expectation for a binomial distribution:
    E(X) = np
  41. The variance for a binomial distribution:
    Var(x) = npq
  42. The average of the math expectation:
    E(X) = a
  43. The average variance:
    Var (x) with a line on top = V/n
  44. The average standard deviation:
    Image Upload 17
  45. The math formula of the density function:
    fImage Upload 18
  46. The math formula of the distribution function:
    Image Upload 19
Card Set
CS546 Definitions
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