Uniform Distribution - Solving Qc and Qd for Screen Placement | Math Homework

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In summary, the questions 3c and 3d from the provided link require the use of probability to determine the location of a dot on a screen. For question 3c, the dot must be within specific ranges from the bottom and left of the screen. For question 3d, the dot must be within a square 2 cm all the way around the outer full screen. To solve these questions, the assumption is made that the dot's coordinates are independent and that the screen is 20cm x 16cm. The probability of the dot appearing in any 1 cm2 of the screen is calculated and used to find the solutions. It is important to show working in order to receive credit for the answers.
  • #1
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Homework Statement



http://www.xtremepapers.com/Edexcel/Advanced%20Level/Mathematics/Subject%20Sorted/S2/Solomon/Solomon%20B.pdf

Questions 3c and 3d

Homework Equations


The Attempt at a Solution


ok so for Qc) it must be between 6 and 10 cm from the bottom and 8 and 12 cm from the left

d) it must be within a square 2 cm all the way around the outer full screen

But I don't see how to calculate the answers - there are an infinite number of solutions
 
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  • #2
Prefacing everything with "Assuming X and Y are independent"... and for extra deviousness, "and that the screen is 20cm x 16cm".

For c), it occupies 1/5 of the horizontal distance and 1/4 of the vertical distance.

For d), take a clue from above and work out the probability of a dot appearing in any 1 cm2 of the screen.
 
  • #3
ok so c) 1/20

d) any 1 cm2 = 1/320
(16*20)-(16*12) = 128
1/320 * 128 = 2/5

is that right?
 
  • #4
apart from needing some explanatory text, looks ok
 
  • #5
what explanatory text
 
  • #6
To quote the front page of the paper:

Advice to Candidates
You must show sufficient working to make your methods clear to an examiner.
Answers without working will gain no credit.
 
  • #7
me sad
but thanks for that!
 

1. What is a uniform distribution?

A uniform distribution is a probability distribution in which every outcome has an equal chance of occurring. It is often visualized as a flat, rectangular shape on a graph.

2. What is Qc and Qd in relation to screen placement?

Qc and Qd refer to the coordinates of a screen's center point on the horizontal and vertical axes, respectively. These coordinates are used to determine the placement of the screen within a given area in order to achieve a uniform distribution of the screen's brightness.

3. How do you solve for Qc and Qd?

To solve for Qc and Qd, you need to first determine the total area that the screen will cover. Then, divide that area by the number of screens in order to calculate the area per screen. Finally, use this value to find the coordinates of the center point on the horizontal and vertical axes.

4. Why is it important to achieve a uniform distribution for screen placement?

A uniform distribution of brightness ensures that viewers will have a consistent viewing experience, as there will be no significant variations in brightness across the screen. This is especially important for large screens or screens used for public displays, as a non-uniform distribution can be distracting and affect the overall quality of the display.

5. Are there any limitations to using a uniform distribution for screen placement?

While a uniform distribution can result in a consistent viewing experience, it may not always be the most optimal placement for certain types of content or viewing angles. In these cases, alternative placement strategies may need to be considered to achieve the desired display quality.

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