Derivative : A derivative of $f$ also written as $f^{\prime}$ or $\frac{d}{dx}f$ or $\frac{df}{dx}$ is defined by $f^{\prime}(x)=\lim \limits_{h\to 0}\frac{f(x+h)-f(x)}{h}.$ The derivative $f^{\prime}(x)$ can be interpreted as the speed at which the function value is changing or as the slope of the tangent in the graph of $f$ at $x$. For example the derivative of a constant function is 0, the derivative of $f(x)=x$ is 1 and the derivative of $x^2$ is $2x.$ All local extrema of differentiable functions $f$ are roots of the derivative of $f.$

Quotient rule : The quotient rule is a rule to calculate the derivative of a function $(\frac{g}{h})$ by using $(\frac{g}{h})^{\prime}=-\frac{gh^{\prime}}{h^2}+\frac{g^{\prime}}{h}.$

Squared : $x$ squared refers to the number $x^2=x\cdot x.$ For example 3 squared equals 9.

Distribution : The distribution of a random variable $X$ refers to how likely $X$ is to take on specific values. If $X$ has values in $\mathbb{R}$ the distribution of $X$ can be described by the function $f(x)=P[X\leq x].$

Normal distribution : A normal distribution with mean $\mu$ and standard deviation $\sigma$ is the distribution with the density given by $\frac{1}{\sqrt{2\pi\sigma^2}} e^{-\frac{(x-\mu)^2}{2\sigma^2}}$ A special property of the normal distribution is that the sum of two normally distributed random variables again has a normal distribution.

Random variable : A random variable $X$ describes all the possible outcomes of a random experiment. The probability distribution of $X$ describes how likely all these outcomes are.

Standard deviation : The standard deviation of a random variable $X$ often denoted by $\sigma_X$ is the square root of its variance. It is defined as $\sigma_X=\sqrt{E[(X-E[X])^2]}=\sqrt{E[X^2]-E^2[X]}.$ The standard deviation is a measure for how far outcomes of $X$ will typically deviate from the mean $E[X].$

Variable : A letter in an expression or function that represents an arbitrary number.

Variance : The variance $var(X)$ of a random variable $X$ is defined by $var(X)=E[(X-E[X])^2]=E[X^2]-E^2[X].$ The variance is the square of the standard deviation of a random variable and is a measure for how far outcomes of $X$ will typically deviate from the mean $E[X].$

Cubed : The cube of a number $x$, or $x$ cubed or $x^3$ is the third power of $x$: $x^3=x\cdot x\cdot x.$ For example 2 cubed equals 8.

Multiplication : Multiplication is the mathematical operation that is a shorthand for adding the same amount several times. For example $3\cdot 4=4+4+4=12.$

Parenthesis : Parenthesis or brackets are used to clarify the order of operations in an expression. Within an expression terms in parenthesis are supposed to be calculated first. For example $2\cdot(3+4)=2\cdot 7=14$ but $2\cdot 3+4=6+4=10.$

Squared : $x$ squared refers to the number $x^2=x\cdot x.$ For example 3 squared equals 9.