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:
denote working, and
denote failed.
The sample space is:
2. Set Operations
Suppose the sample space is:
.
Let:
,
,
and
.
Determine the sets:
Here:
Thus,
So,
3. Natural Numbers Divisibility
Let:
,
the set
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,
Read MoreMastering 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
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
Read MoreCircumference, Ellipse, Parabola, and Hyperbola
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
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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