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MATH-PROB-2: Key Concepts in Probability, Calculus, and Kinematics

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This guide presents essential concepts in probability, calculus, and related areas of mathematics. It distinguishes probability scenarios, such as “with replacement” vs. “without replacement,” and covers discrete random variables, conditional probability, probability distributions, expected value, and uniform distribution. Key calculus concepts include anti-differentiation, average and instantaneous rates of change, derivatives, product and quotient rules, stationary points, inflection points, global maxima and minima, and the second derivative test. The guide also introduces geometric applications, such as inscribed rectangles. In kinematics, fundamental concepts such as acceleration, velocity, displacement, and average speed are defined, along with statistical measures of variability, including variance and standard deviation. It also touches on half-life in physics and marginal profit functions in economics, linking mathematical concepts to real-world applications.

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MATH-PROB-2: Key Concepts in Probability,
Calculus, and Kinematics
with replacement" vs "without replacement" - -with replacement- the item chosen is returned
to the original group, denominator stays the same

-without replacement-the item will not be returned, number of possible outcomes will change
to reflect that

Acceleration - rate of change of velocity

Anti-differentiation - The process of finding a primitive (original) function from the derivative. It
is the inverse operation to differentiation

Asymptote - a line that a graph approaches but never crosses

average rate of change - The rate of change across the interval

average speed - total distance divided by total time

Conditional Probability - the probability that one event happens given that another event is
already known to have happened

discrete random variable - A variable which can only take a countable number of
values

Displacement - Distance and direction of an object's change in position from the starting
point.

exact value - The value of an expression that has not been rounded

expected value - The mean of a probability distribution.

Global Maximum - Finds the highest y-number the function goes to

half-life - the time taken for the radioactivity of a specified isotope to fall to half its original
value.

Inflection Point - A point of a curve at which a change in the direction of curvature
occurs.

inscribed rectangle - a rectangle whose area lies entirely inside a geometric figure or curve; all
vertices of the rectangle lie on the curve
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