A doctor wants to measure the cholesterol level, , of a patient. The hospital ha

Question

A doctor wants to measure the cholesterol level, , of a patient. The hospital has two devices.Device1 gives a reading X1 that has mean and a standard deviation of 5. Device 2, which is more sophisticated and more expensive, gives a reading X2 that has mean and a standard deviation of 2 . The two devices operate independently. The lab technician decides to use the reading given by

Y = 0.2X1+0.8X2

(i.e. he uses both devices but gives more weight to the reading given by Device 2, for an obvious reason).

A. Find the expected value of Y

B. Find the variance of Y

Explanation / Answer

Mean Y = 0.2 * mean(X1) + 0.8* mean(X2) = 0.2u + 0.8u = u

Variance Y = 0.2^2 * var(X1) + 0.8^2*var(X2) = 0.2*0.2*5*5 + 0.8*0.8*2 *2= 3.56

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