Suppose that a surveyor is trying to determine the areas of a rectangular field,

Question

Suppose that a surveyor is trying to determine the areas of a rectangular field, in which the measured length X and the measured width Y are independent random variables that fluctuate widely about the true values, according to the following probability distributions The calculated area A=XY of course is a random variable. What is the expected area? using the information that X and Y are independent. Then find the distribution of XY (X product Y), as we did in the lecture notes). The expectation is computed using that distribution.

Explanation / Answer

WE NEED TO FIND THE EXPECTED AREA OF THE RECTANGULAR

AREA = X*Y

= E(X)*E(Y)

E(X) = X1*P(X1)+X2*P(X2)+....XN*P(XN)

= 8*0.25 +10*0.25 + 11*0.5 = 10

E(Y) = Y1*P(Y1)+Y2*P(Y2)+....+YN*P(YN)

= 4*0.5+6*0.5 = 5

HENCE ARES = 10*5 = 50

THEREFORE OPTION A IS CORRECT.

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