Statistics Cheat Sheet: Key Concepts and Formulas
Find the probability that exactly four of the sampled people own a tablet computer. We input 15 for n, .3 for p, and 4 for x = binompdf(15,.3,4) 15 is sample size .30=30% || To compute P(x), select poissonpdf and enter the values for λt and x separated by commas and press ENTER. || To compute P(Less than or equal to x), select poissoncdf and enter the values for λt and x separated by commas and press ENTER. || Let A and B be events with P(A) = 0.7, P(B) = 0.4, and P(B|A) = 0.2. Find P(A and B)
Read MoreUnderstanding Uncertainty and Reliability in Structural Design
Q1. Uncertainty and Safety Factors in Structural Design
(a) Types of Uncertainty
i. Aleatory Uncertainty
Aleatory (Random or Objective) uncertainty, also known as irreducible or inherent uncertainty, is the intrinsic randomness of a phenomenon. Think of rolling dice – the outcome is inherently unpredictable.
ii. Epistemic Uncertainty
Epistemic (Subjective) uncertainty is reducible uncertainty stemming from a lack of knowledge or data. As we gather more information, this type of uncertainty decreases.
Read MoreTransformations of Functions and Mathematical Concepts
Transformations: g(x) = af(b(x+c))+d
Parameters and Their Effects
a
- a > 1: Vertical stretch
- 0 < a < 1: Vertical compression
- a < 0: Vertical reflection
b
- b > 1: Horizontal compression
- 0 < b < 1: Horizontal stretch
- b < 0: Horizontal reflection
c
- c > 0: Shift left
- c < 0: Shift right
d
- d > 0: Shift up
- d < 0: Shift down
Examples
g(x) = f(x-3) – 1: Horizontal shift right 3 & vertical shift down 1
h(x) = -f(x): Vertical reflection
j(x) = f(-2(x+3)) + 1: Horizontal reflection, horizontal
Read MoreExam 2 Review: Finance Concepts and Calculations
Exam 2 Review
Chapter 5: Time Value of Money (Practice quizzes, MindTap, and class examples)
Key Concepts
- Future Value (FV): Represents the value of an investment at a specific future date, considering interest earned.
- Simple Interest: Interest earned only on the principal amount. FV = PV + PV(I)(N)
- Compound Interest: Interest earned on both the principal and accumulated interest. FV = PV x (1+I)^n
- Compounding: The process of converting present values into future values.
- Discounting: The process of converting
Direct Proof and Counterexample I: Introduction to Proof Techniques
Section 4.1 – Direct Proof and Counterexample I: Introduction
Discovery and Proof
Discovery and proof are integral parts of problem-solving. When you believe a statement is true, try to understand why. Success validates your discovery, while failure provides insights into the problem and may reveal the statement’s falsity.
Assumptions
- This text assumes familiarity with basic algebra laws (see Appendix A).
- We utilize the three properties of equality: For all objects A, B, and C, (1) A = A, (2) if A
Teachers’ Perceptions & Practices of Teaching Math Through Problem Solving in Senior High School
Teachers’ Perceptions & Practices of Teaching Mathematics Through Problem Solving in the Senior High School
Student Information
Student Name: Elvis Owusu
Student Number: 8110110016
Course Name: MPhil Mathematics Education
Department: Mathematics
Supervisor: Dr. M.J. Nabie
Chapter 1: Introduction
Overview
This chapter provides context for the study, outlining the background, problem statement, purpose, significance, research questions, delimitations, and limitations.
Background of the Study
Mathematics
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