A function f(x) is a valid probability density function (PDF) if: Uniform distribution expected value:(a + b)/2
f(x) ≥ 0 for all values of x. Standard normal distribution: P (a ≤ X ≤ b)= Φ(b) − Φ(a)
∫ −∞∞ f(x)dx = 1. General Form of a Taylor Polynomial:
Pn(x) = f(a) + f'(a)(x - a) + [f''(a)/2!](x-a)2 + [f'''(a)/3!](x-a)3 + ... + [f(n)(a)/n!](x - a)n
Maclaurin series formula:
3.1 7 types of electro magnic
gamma-ray-highly energetic form of electromagnetic radiation. uv-nails and skin cancer. infared- night vision, help see if painting fake. x-ray- see inside you or bones. Microwave- cook food and can go outer space. visible light -the portion of the electromagnetic spectrum that the human eye can perceive radio wave-a type of electromagnetic radiation that exist in the lowest frequency,
...Here's a concise and exam-ready answer for your notes:
Definition:
Cost of capital is the minimum rate of return that a business must earn on its investments to maintain its market value and attract funds. It represents the opportunity cost of using capital in one investment over another with similar risk.
Investment Decisions (Capital Budgeting):
Used as a discount rate in evaluating investment projects (NPV, IRR). A project is accepted
"The present was an egg laid by the past that had the future inside its shell."
Part I: Why I Chose This Quote
I chose this quote because it captures the flow of time in a powerful and poetic way.
It reminded me that nothing exists in isolation — everything happening now is a result
of something that came before, and everything we do now shapes what’s coming next.
Personally, it made me think about how my own life is constantly being shaped by past
experiences, decisions,
Aim: To estimate the protein using Lowry’s method.
Principle: The –CO-NH- bond (peptide) in polypeptide chain reacts with copper sulphate in an
alkaline medium to give a blue colored complex. In addition, tyrosine and tryptophan residues of
protein cause reduction of the phosphomolybdate and phosphotungstate components of the Folin-
Ciocalteau reagent to give bluish products which contribute towards enhancing the sensitivity of
this method.
Reagents Required:
1. Reagent A: 2% sodium carbonate...
1. What is meant by vouching (2 marks)
Vouching refers to the process of checking the authenticity of transactions recorded in the books of accounts using supporting documents. It ensures accuracy and reliability in financial reporting.
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2. Features of a good internal check system (5 marks — 6 points)
1. Division of work: Duties are distributed to prevent overlapping.
2. Checks and balances: One employee’s work is automatically checked by another.
3. Responsibility fixing: Each employee
Contribution of Saint Simon in Sociology
Henri de Saint-Simon (1760–1825), a French thinker, is considered one of the early founders of sociology. Though not a sociologist in the modern sense, his ideas laid important groundwork for the development of the discipline. His work focused on society, social change, industrial development, and the role of science in social progress. Major Contributions of Saint-Simon:
1. Founding Father of Social Science : Saint-Simon is considered among the first
...These protocols help in uniquely identifying devices in an IoT system so that each device can be tracked, authenticated, or managed.
Each IoT device needs a unique IP address.
IPv6 supports trillions of addresses, ideal for billions of IoT devices.
Devices can auto-generate their address using SLAAC (Stateless Address Auto Configuration).
Used in RFID systems.
Uniquely identifies
Physical Adsorption (Physisorption): 1.It occurs due to weak van der Waals forces between the adsorbent and adsorbate. 2.The enthalpy of adsorption is low, typically between 20–40 kJ/mol. 3.It is usually non-specific and can occur on many types of surfaces. 4.It is reversible in nature and can be undone by changing pressure or temperature. 5.Physisorption is favored at low temperatures. 6.It can result in the formation of multiple layers of adsorbed molecules. 7.Little to no activation energy