Find X m 1 m 2 m 3 m 4
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
![### Educational Exercise: Circles and Angles
**Context**
This exercise involves a circle with various points marked and angles labeled. We'll analyze the relationships between these angles and the arcs they intercept.
**Diagram Explanation**
A circle is drawn with center point O. Several other points are located on the circumference and connected with line segments, forming chords:
- Points A, B, C, and D lie on the circumference of the circle.
- Angles within the circle are labeled with numeric identifiers 1, 2, 3, and 4.
Line segments:
- AC, AB, AD (tangent to the circle at point B), BD
- Three arcs are defined by these points: Arc AC (2x), Arc AB (4x), and Arc CD (3x)
### Notations and Labels
- **Angles inside the circle**:
- ∠AOB is labeled as angle 1
- ∠BOD is labeled as angle 2
- ∠AOD is labeled as angle 3
- ∠COD is labeled as angle 4
- **Arcs**:
- Arc AC is labeled as 2x
- Arc AB is labeled as 4x
- Arc CD is labeled as 3x
### Instructions for Students
Given this diagram:
- **Identify and calculate the angles and arcs:**
- Use the relationships between the arcs and angles to find missing information.
- Recall that the measure of an angle formed by two chords intersecting inside a circle is half the sum of the measures of the arcs intercepted by the angle and its vertical angle.
- Apply properties of circles such as the Inscribed Angle Theorem, properties relating to tangents, secants, and chords.
### Additional Notes
This exercise is designed to test students' ability to synthesize knowledge about circles, angles, and their relationships. Please ensure to write clear steps and show all workings to substantiate your answers.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50878265-07d3-4d89-b183-366bd73e3337%2Fa2b477ee-41f8-42b4-a8f5-a8a9e4b3e38d%2Fcrfoaa8_processed.jpeg&w=3840&q=75)
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