Finding constant related to random variable

In summary, the conversation discusses the value of a in the equation Var(Y) = a^2 * Var(X), where Var(X) and Var(Y) are given values. It is stated that the answer key only accepts a value of 0.8, not -0.8, despite there being two possible pairs of a and b. The conversation also mentions the importance of maintaining a positive scaled mark and the potential negative impact of using -0.8 as the value of a.
  • #1
songoku
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Homework Statement
Exam marks, X, have mean 70 and standard deviation 8.7. The marks need to be scaled using the formula Y = aX + b so that the scaled marks, Y, have mean 55 and standard deviation 6.96. Find the values of a and b
Relevant Equations
E(aX + b) = a.E(X) + b

Var(aX + b) = a^2 Var (X)
Var (Y) = a2 . Var (X)
(6.96)2 = a2 . (8.7)2
a = ± 0.8

But the answer key states that the value of a is only 0.8

Why a = -0.8 is rejected? Thanks
 
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  • #2
songoku said:
Why a = -0.8 is rejected?
Why do you think?
 
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  • #3
PeroK said:
Why do you think?
In my opinion, there are two possible pairs of a and b so a = -0.8 is possible
 
  • #4
songoku said:
In my opinion, there are two possible pairs of a and b so a = -0.8 is possible
What do you want the mean to be?
 
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  • #5
You are correct in saying that the -0.8 would give the correct mean and variance, but the term "scaled" is assumed to imply that the values of X are just shifted and stretched/shrunk -- not reversed.
 
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  • #6
songoku said:
Why a = -0.8 is rejected?
I would be very angry if my raw score (X) on the exam was 70, but my adjusted score wound up being -56.
 
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  • #7
Mark44 said:
I would be very angry if my raw score (X) on the exam was 70, but my adjusted score wound up being -56.
The proposed formula is ##Y = -0.8X + 111##. Your score of##70## would, indeed, scale to the average of ##55##. But a score of ##80## would scale to ##47##.
 
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  • #8
PeroK said:
What do you want the mean to be?
For a = -0.8 and b = 111, the mean for Y is 55

Mark44 said:
I would be very angry if my raw score (X) on the exam was 70, but my adjusted score wound up being -56.
Well, I won't because my peers' scores will also be negative :biggrin:

Besides, there is still value of b to make the scaled mark positive

FactChecker said:
You are correct in saying that the -0.8 would give the correct mean and variance, but the term "scaled" is assumed to imply that the values of X are just shifted and stretched/shrunk -- not reversed.
I understand the assumption

Edit: I just saw post #7. That is indeed does not make sense

Thank you for all the help and explanation PeroK, FactChecker, Mark44
 
  • #9
And the first one now will later be last ...
 
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Related to Finding constant related to random variable

1. What is a constant related to a random variable?

A constant related to a random variable is a numerical value that remains the same throughout all possible outcomes of the random variable. It can also be referred to as a fixed value or a parameter.

2. How is a constant related to a random variable determined?

A constant related to a random variable is typically determined through mathematical calculations or statistical analysis. It can also be based on prior knowledge or assumptions about the random variable.

3. What is the significance of finding a constant related to a random variable?

Finding a constant related to a random variable is important because it allows for the prediction and analysis of the behavior of the random variable. It can also help in making decisions and drawing conclusions based on the data collected.

4. Can a constant related to a random variable change?

No, a constant related to a random variable remains the same throughout all possible outcomes of the random variable. However, it can be updated or revised if new information or data is obtained.

5. How does a constant related to a random variable differ from a random variable itself?

A constant related to a random variable is a fixed value, while a random variable is a variable that can take on different values based on chance or probability. A constant is used to describe the behavior of a random variable, while a random variable is the actual entity being studied or observed.

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