Probability and Statistics: Solved Problems

Assignment A

1. Electrical Unit Failure Analysis

An electrical unit consists of four components, each subject to failure. We observe this unit at a specified time to determine which components are working and which have failed. What is the sample space associated with this random experiment?

Let: 7TVxAAAAMklEQVQYV2NgIAVwMwoKMQlyMzIASQEg denote working, and 7TVxAAAAOElEQVQYV2NgQAdCrExAIVE2fm4gJcgO denote failed.

The sample space is:

sk1Po1IGBDvwBSXFyLLSZGa0AAAAASUVORK5CYII

r0FVpCrlQq1hbtYj4GRDuBWRUyNYkTTre+ULPpX+

2. Set Operations

Suppose the sample space is: w8MgooHMhmQAAAAASUVORK5CYII= . Let: Ah3KH1ZdVC6IAAAAAElFTkSuQmCC , P7QsOtpxon0ScHGICU69ueneJYv4B4EfzfMfJs+B , and GVqf0R6ASYXx9u0HKKzAAAAABJRU5ErkJggg== .

Determine the sets: rJ4EMhaCNY2UvgAAAABJRU5ErkJggg==

Here: 1D3L2AXFUIWU9OyTQYAAAAASUVORK5CYII=

QAAAABJRU5ErkJggg==

Thus, s1c+AZFgH4yljD1VAAAAAElFTkSuQmCC

So, 5L3W4yP8V+QmWmTt3MOHHfAAAAABJRU5ErkJggg=

3. Natural Numbers Divisibility

Let: Zu4Tlr8b3J6NIswAAAAASUVORK5CYII= , 7TVxAAAAQElEQVQoU2NgoAAIc3Gi6xZgY0cTEuIQ the set

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Lobende SRL Discount Policy: Maximize Your Savings

Lobende SRL Discount Policy

The discount policy of Lobende SRL is as follows:

If a client makes purchases exceeding €1,000 within a month, a 10% discount is applied, unless they are considered a bad-paying customer. In that case, monthly purchases must exceed €2,000 to qualify for the 10% discount. To further increase market penetration, the aforementioned discounts are increased by 10% for all internal customers. Finally, a 15% discount is applied to customers who purchase more than €2,000,

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Mastering Math Operations: Signs, Powers, and Roots

Rules of Signs: Multiplication and Division

  • (+) × (+) = (+) Positive multiplied by positive equals positive.
  • (+) × (−) = (−) Positive multiplied by negative equals negative.
  • (−) × (+) = (−) Negative multiplied by positive equals negative.
  • (−) × (−) = (+) Negative multiplied by negative equals positive.
  • (+) ÷ (+) = (+) Positive divided by positive equals positive.
  • (+) ÷ (−) = (−) Positive divided by negative equals negative.
  • (−) ÷ (+) = (−) Negative divided by positive equals
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Variables, Hypotheses, Measurement, and Research Purposes

Variables and Hypotheses

An independent variable is thought to influence, affect, or cause variation in another variable. A dependent variable is thought to depend upon or be caused by variation in an independent variable.

Antecedent Variable: An independent variable that precedes other independent variables in time. It could affect the independent variable and alter its relationship to the dependent variable.

Intervening Variable: If the relation between X and Y is not spurious, then the intervening

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Properties of the Circumference

The circumference is generated by the intersection of a cylinder or a straight circular cone with a plane. Geometrically, the circumference has several elements, such as:

  • Center: A fixed point equidistant to all points of the circumference.
  • Radius: The distance of the segment that joins the center of the circumference to any of its points.
  • Chord: The segment that joins any two points of the circumference.
  • Diameter: The chord that passes through the center and has the maximum
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Key Equations and Concepts in Mathematics

Parallel = Original equation. PP = – Reciprocal

x = (-b ± √(b^2 – 4ac)) / (2a), complex solutions. Vertex = (-b) / (2a)

(x/2)^2. If a > 0, then the parabola opens up.

Parabola form = a(x – h)^2 + k. If a < 0, then the parabola opens down.

P = 2L + 2W

x + x + z = y

A = L * W

N = odd and an > 0 = Falls Left + Rises Right

N = odd and an < 0 = Rises Left + Falls Right

N = Even and an > 0 = Rises Left + Rises Right

N = Even and an < 0 = Falls Left + Falls Right

Rational zero = P/Q

Factor = x

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