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Math Help - Some help required please

  1. #1
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    Some help required please

    Here is the Q)

    You have two instruments (1 and 2) to measure the height of a building. Suppose the buildings true height is 120 metres. Measurements with Instrument 1 vary with a mean of 120m and a standard deviation of 1.2m. Measurements with Instrument 2 vary with a mean of 120m and a standard deviation of 0.85m.

    You make one measurement with each instrument. Let X1 = your measurement using Instrument 1 and X2 = your measurement using instrument 2.

    Random variable W = measurement variable where:


    W = 1/3 * X1 + 2/3 * X2

    A) Calculate the mean of W
    B) Find the standard deviation of W.



    Im unsure as to what X1 and X2 are considering i have 2 measurements for each instrument.

    Any help appreciated thanks.
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  2. #2
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    Quote Originally Posted by Dogfighters View Post
    Here is the Q)

    You have two instruments (1 and 2) to measure the height of a building. Suppose the buildings true height is 120 metres. Measurements with Instrument 1 vary with a mean of 120m and a standard deviation of 1.2m. Measurements with Instrument 2 vary with a mean of 120m and a standard deviation of 0.85m.

    You make one measurement with each instrument. Let X1 = your measurement using Instrument 1 and X2 = your measurement using instrument 2.

    Random variable W = measurement variable where:


    W = 1/3 * X1 + 2/3 * X2

    A) Calculate the mean of W
    B) Find the standard deviation of W.



    Im unsure as to what X1 and X2 are considering i have 2 measurements for each instrument.

    Any help appreciated thanks.
    Are X1 and X2 independent? If so, note that E(aX_1 + bX_2) = aE(X_1) + bE(X_2) and Var(aX_1 + bX_2) = a^2Var(X_1) + b^2 Var(X_2).
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