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: