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Math Help - find the Variance

  1. #1
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    find the Variance

    is known that the Tomato crop (in ton) in some farm are Sampled for 10 years.
    the Standard deviation of the crop was 2 ton.
    the Income (Y) from the Tomato Depends on the crop (X)
    according to following connection Y=3X-2. the Variance Income from the Tomato in this Sampled is ?

    if i know that the Standard deviation is 2 so i just need to do 2^2 to get the Variance yes?

    and 1 more Question: the Value of Pearson product-moment correlation coefficient between the crop and the Income is?
    how i can solve it?

    thanks.
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  2. #2
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    Quote Originally Posted by ZOOZ View Post
    is known that the Tomato crop (in ton) in some farm are Sampled for 10 years.
    the Standard deviation of the crop was 2 ton.
    the Income (Y) from the Tomato Depends on the crop (X)
    according to following connection Y=3X-2. the Variance Income from the Tomato in this Sampled is ?

    if i know that the Standard deviation is 2 so i just need to do 2^2 to get the Variance yes?

    and 1 more Question: the Value of Pearson product-moment correlation coefficient between the crop and the Income is?
    how i can solve it?

    thanks.
    The formula for Var(aX + b) should be given in your textbook or class notes. Have you looked for it? (You will also find it using Google).

    The procedure for calculating the Pearson product-moment correlation coefficient should also be given in your class notes or textbook (or found using Google). Where are you stuck?
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  3. #3
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    well

    i am not study this in class yet, this why i asked it here.

    tell me if i correct if i will say that the Variance will be 4 because the Standard deviation of the crop was 2 ton, so i only need to do 2^2=4 yes?

    and for Pearson product-moment correlation question can you give me any direction?

    thank you.
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  4. #4
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    Quote Originally Posted by ZOOZ View Post
    i am not study this in class yet, this why i asked it here.

    tell me if i correct if i will say that the Variance will be 4 because the Standard deviation of the crop was 2 ton, so i only need to do 2^2=4 yes?

    and for Pearson product-moment correlation question can you give me any direction?

    thank you.
    Perhpas it would be best to wait until you have started your studies in this class. That way, your teacher can give you the instruction you need to understand how to answer questions like these.
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  5. #5
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    :) ok maybe you are right

    still thank you.
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  6. #6
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    well i still want to try one more try:
    if is known that the Standard deviation of the crop(X) was 2 ton so the Variance of it will be 4 so if i use Y=3X-2 and put there those numbers:
    Y=3*4-2=10 so the Variance Income from the Tomato in this Sampled will be 10 ?

    thanks.
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  7. #7
    MHF Contributor Unknown008's Avatar
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    No, it's a little more complicated than that.

    If you have

    Y = aX + b

    where a and b are constants;

    Var(Y) = Var(aX + b)

    Var(Y) = Var(aX) + Var(b)

    Var(b) is zero because the variance of a constant is zero, right?

    So, Var(Y) = Var(aX)

    Here is something to be careful, Var(aX) = a^2Var(X)

    So,

    Var(Y) = a^2Var(X)
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  8. #8
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    OK so if i use this:var(aX+b)=a^2var(X)
    i get 9*4=36 and this is the answer ?
    "ar(b) is zero because the variance of a constant is zero, right" that was helping.

    thanks.
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  9. #9
    MHF Contributor Unknown008's Avatar
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    Yes, that is the variance of Y.
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  10. #10
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    GREAT.

    thank you very much.
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  11. #11
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    hi.
    according to the same information that i gave in this question i can say that the Pearson correlation coefficient will be 1
    because we have Absolute linear relationship.

    i almost sure is 1 but about the reason i not sure 100%.

    thanks.
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