Algebra
The roots of the following equation:
15x2-x-28=0
What is (x=-4/3 or 7/5) ?
The derivative of the following function:
f(x) = 10(4x2+8x-13)13
What is
130(8x+8)(4x2+8x-13)12
The mathematical formula for standard error of the mean.
What is std. dev. / sqrt(N)?
What is 0.510
How many grains of sand are on all the beaches on Earth?
~10^20
The solution of the following system:
-2x-3y=4
3x+y=0
What is x=4/7 and y=-12/7 ?
Calculate the integral of the following function:
f(x) = xln(x)
What is
-1/4?
The expected value of a fair six-sided die rolled once, where you win $5 if the result is a 6, $2 if the result is a 4 or 5, and $0 otherwise.
What is $1.50?
The variance of a Bernoulli random variable.
What is p(1-p)?
How many heartbeats occur in an average human lifetime?
~3*10^9
This value tells us whether a square matrix is invertible.
What is a determinant?
Calculate the integral of the following function:
f(x) = (x+4)/((x)(x2+5x+6))
What is
-ln|x+3|+2ln|x+2|+C ?
The measure of how well a regression model explains variation in a dependent variable.
What is R^2?
Independence of Events
What is P(A ∩ B)=P(A)P(B)?
How many piano keys exist in the world?
~10^8
The rank of the following 5x5 matrix:
[1 5 -2 -1 1]
[2 1 -1 -2 -1]
[0 2 3 0 8]
[-1 0 3 1 6]
[-1 3 -2 1 -1]
3
This determinant measures how area or volume scales under a transformation.
What is the Jacobian?
The Cauchy Distribution is a special case of this distribution when the degrees of freedom is equal to 1.
What is the Student t distribution?
What is P(x=k) = e-lambda*lambdak/k!.
How much energy does the Sun emit every second?
~4 x 10^29 J/s
A group with a commutative operation is called this.
What is an Abelian group?
In Multivariable Calculus, this method allows you to convert a function in any dimension to a single variable?
What is parameterizing by t?
Let A be an estimator of a population with mean M with A=(2a+b+c+...+z)/10. This is the kind of estimator A is.
On a game show, you pick one of three doors. A car is behind one, and goats are behind the other two. The host, who knows where the car is, opens one of the two doors you didn't pick, revealing a goat. He then asks if you want to stick with your original choice or switch to the other unopened door. This is the probability you win the car if you switch.
What is 2/3?
How many air molecules are in this classroom?
~10^27