# Math Help - Some help required please

1. ## 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.

2. Originally Posted by Dogfighters
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 $Var(aX_1 + bX_2) = a^2Var(X_1) + b^2 Var(X_2)$.