With reference to the Example 30, for a problem diagnosed as being due to an incomplete initial repair, find the probability that the initial repair was made by

(a) Tom;

(b) Georgia;

(c) Peter.

Data From Example 30

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EXAMPLE 30 Variances of X - X2 and X + X2 when X, and X2 are independent Let X have mean 1 and variance and let X2 have mean 2 and variance 2. Find the mean and variance of (a) X1 X2 and (b) x1 + x2 if X1 and X2 are independent. Solution (a) Note that X - X2 is of the form aX + a2X2 with a = -a2 = 1 so it has mean and variance 1 + (-1) = - (1). o +(-1) = 0} } +0 2 (b) Since X1+X2 corresponds to the case with a = a2 = 1, it has mean 1[+12 = + and variance . + =