The flashcards below were created by user
Kevinpom
on FreezingBlue Flashcards.
-
What is the definition of a derivative?
Limit as delta-x approaches zero of:
- delta-x
-
What is the domain of a function?
All the values that can be plugged into an equation.
-
What is the range of a function?
All the values that can come out of a function.
-
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.
-
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.
-
Where do vertical assymptotes occur?
Where the function is undefined.
-
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
-
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).
-
How do you find the area under a curve that goes to infinity?
Take the limit of the integral as x--> infinity.
-
Where do inflection points occur?
Where the second derivative = 0.
-
What does n stand for in a statistics equation?
The number of trials that will be performed.
-
What does k stand for?
- How many times there is a positive outcome.
- Or
- The number of trials until the event has occured.
-
What does p stand for?
The probability of a positive outcome.
-
What does q stand for?
The probability of the a negative outcome (1-p).
-
What is the formula of the Geometric Distribution?
-
What is the probability of a positive result in a single trial in a Geometric Distribution? (math expectation)
p
-
What is the math expectation in a Geometric Distribution?
-
What is the formula of Standard Deviation? ( )
-
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.
-
How do you find the expectation, E(X) of a density function?
For a continuous random variable.
-
What is the formula for Variance? Var(X)
-
What Kind of Distribution is used for a situation where x can take on an infinite number of values?
Continuous or Normal Distribution.
-
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.
-
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:
-
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:
-
The probability of A and B occurring:
-
The probability of A or B occurring:
-
What is a discrete variable?
A variable with a countable number of outcomes
-
What is a continuous variable?
A variable with an infinite number of outcomes.
-
The cumulative distribution notation:
F(X)
-
The density function notation:
f(x)
-
How do you go from the density function to the continuous random variable?
Take the integral from - infinity to infinity (usually in three sections)
-
How do you go from the continuous function to the density function?
Take the derivative (usually three sections)
-
When can you not use the binomial distribution?
When n is very large.
-
What do you use when n is very large and the probability is >0.1?
- The Normal approximation:
 etc...
-
If n is large and p(A) is very small (<0.1) we use:
- The Poisson distribution.
-
The formula for the math expectation:
-
The sum of the math expectation:
-
The product of the math expectation:
-
The formula of the math expectation for a binomial distribution:
E(X) = np
-
The variance for a binomial distribution:
Var(x) = npq
-
The average of the math expectation:
E(X) = a
-
The average variance:
Var (x) with a line on top = V/n
-
The average standard deviation:
-
The math formula of the density function:
f 
-
The math formula of the distribution function:
|
|
