Understanding Mathematical Functions: Key Concepts and Definitions
RELATIONSHIP: A relationship exists between two sets if there is a link between them. These sets may be different or may occur within the same set.
ROLE: This is a relationship with two key features:
- Existence: For each element of the set of departure, there is another element in the set of arrival to which it is linked.
- Uniqueness: Each element of the set of departure is bound to a single element in the set of arrival.
SET OF DEPARTURE: The first set involved in the relationship.
SET OF ARRIVAL: The
Read MoreKey Math Concepts: Definitions and Theorems
A magnitude is anything that can be measured or counted.
Direct and Inverse Proportionality
Magnitudes directly proportional: If one magnitude is multiplied by a number, the other is divided by the same number automatically. For example, speed and time are inversely proportional; their product is constant.
Magnitudes inversely proportional: If one magnitude is multiplied or divided by a number, the other is divided or multiplied by that number, respectively.
Sequences
A sequence is an infinite set of
Read MoreAlgebraic Expressions, Equations, and Identities
Algebraic Expressions
An algebraic expression is a combination of numbers and letters connected by arithmetic operation signs. The letters are called variables.
Monomials
A monomial is an algebraic expression where the only operations affecting the variables are multiplication and natural exponentiation. Monomials with the same literal part are like terms.
Polynomials
A polynomial is an algebraic expression formed by the sum or difference of two or more monomials. The degree of a polynomial is the highest
Read MoreSix Sigma and Statistical Process Control: Key Concepts
78) Which step of the Six Sigma DMAIC procedure monitors the process to make sure high performance levels are maintained?
E) Control
79) Which step of the Six Sigma DMAIC procedure involves identifying data sources and preparing a data collection plan?
B) Measure
80) Six Sigma teachers can attain different level titles, based on their experience and level of achievement. What is the highest level a Six Sigma teacher can reach?
C) Master Black Belt
81) In acceptance sampling, the proportion defective that
Read MoreUnderstanding Gradient Descent and Regression Techniques
Gradient DescentDefinition: An optimization algorithm used in machine learning to minimize the cost function of a model by iteratively adjusting its parameters in the opposite direction of the gradient. How Does Gradient Descent Work?
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Probability and Statistics Problems: A Comprehensive Set
1. Four-Digit Lock
(a) How many combinations are made with the first digit 1 or 2 and digits repeat?
(b) If the first digit is 1 or 2, what is the probability of all digits being unique?
2. Probability Mass Function (PMF) Table
(a) Present the cumulative distribution function (CDF) of X.
| 0 | 1 | 2 | 3 | 4 | 5 | |
|---|---|---|---|---|---|---|
| PMF | 0.1 | 0.1 | 0.25 | 0.4 | 0.1 | 0.05 |
(b) Compute E(X) and STD(X).
(c) If a day pass is $5, how much is spent on the trolley?
3. Flight and Luggage Problem
Leah is flying from Boston to Denver with a connection in Chicago. The
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