Numerical Methods: A Comprehensive Guide to Algorithms and Techniques
Floating Point Representation
Floating point representation is a method used to represent real numbers in a way that can accommodate a wide range of values. It expresses numbers in the form ±𝑚×2𝑒, where 𝑚 is the mantissa (or significand), 𝑒 is the exponent, and the base is typically 2 in binary systems. Floating point numbers can represent very large or very small values but with a trade-off in precision. The precision depends on the number of bits allocated to the mantissa, while the
Read MoreConcepts in Artificial Intelligence and Logic
Probabilistic Reasoning
Definition
Probabilistic reasoning is a method used in artificial intelligence to handle uncertainty by quantifying the likelihood of different outcomes or events based on available evidence and prior knowledge.
Probabilistic Models
Probabilistic reasoning involves using probabilistic models, such as Bayesian networks or Markov models, to represent and reason about uncertain situations. These models capture dependencies between variables and assign probabilities to different
Read MoreStatistics Fundamentals: Sampling, Probability, and Hypothesis Testing
Populations, Samples, and Parameters
A population encompasses all items (data) relevant to a study, while a sample is a subset drawn from this population. A parameter describes a population characteristic, whereas a statistic describes a sample characteristic.
Conducting a census (surveying the entire population) can be expensive and time-consuming. Therefore, sampling methods are employed.
Types of Sampling Plans
- Simple Random Sampling: Every possible sample of the same size has an equal chance of
Consumer Behavior Exam Preparation Guide
Important Information (Must Know for Exam)
1a) – one page
1b) – write on another page
No need writes until the end
Consumer Behavior – (Whole) Definition
Needs and Wants
One whole question on Motivation. (Lecture 2A, Slide 4) might come up in exam
Nature of Motivation
Consumption Patterns / Profile of Consumers Changed Over the Last 10-15 Years. (Exam Ask for at Least 10)
Important Thing: Critiques (Under Criticisms of Maslow’s Theory)
- Everybody has 5 levels of needs.
- How to use hierarchy needs in marketing?
Circling the Square and Approximating the Square Root of 2: Exploring the Baudhayana Shulbasutra
Circling the Square – Baudhayana Shulbasutra
This method describes how to construct a circle with an area equal to that of a given square.
It means we have to convert or construct a circle equal to the square.
-> By Pythagoras, OA’ = √(a2+a2)
OA = √(2a2) = a√2
-> Here OA=OE=√2
-> Make a point F, such that OF= OG+1/3GE
-> Draw a circle with center F and radius OF. This circle’s area is equal to the square’s area.
Proof
OF= OG+1/3GE
OF=a+1/
Read MoreMeasures of Dispersion and Correlation in Statistics
Measures of Dispersion
Range
Strengths:
- Simplicity: Easy to understand and calculate.
- Quick Insight: Provides a quick indication of the spread between the minimum and maximum values.
Weaknesses:
- Sensitivity to Outliers: Heavily affected by extreme values, making it less reliable for skewed distributions.
- Ignores Middle Data: Does not consider the distribution of data points between the extremes.
Variance
Strengths:
- Incorporates All Data: Takes into account every data point in the dataset.
- Foundation for Other