Let X1, X2, and X3 represent the times necessary to perform three successive repair tasks at a certain service facility. Suppose they are independent normal random variables with expected values mu1-mu2-mu3-65 and variances sigma1 2-sigma2 2-sigma3A2-20 respectively. What is the value of VIX1+X2-X3]? 20 40 60 80 195 260

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16-12-2022
Mathematics

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Let X1, X2, and X3 represent the times necessary to perform three successive repair tasks at a certain service facility. Suppose they are independent normal random variables with expected values mu1-mu2-mu3-65 and variances sigma1 2-sigma2 2-sigma3A2-20 respectively. What is the value of VIX1+X2-X3]? 20 40 60 80 195 260

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durbansa43 durbansa43 · Answer 1 · 2022-12-20T12:07:33-05:00

C. 60

To find the variance of the sum of three independent random variables, you can use the formula for the variance of the sum of independent random variables.

Var(X1 + X2 + X3) = Var(X1) + Var(X2) + Var(X3)

The variances of X1, X2, and X3 are given as sigma1^2, sigma2^2, and sigma3^2 respectively, so the variance of X1 + X2 + X3 is

Var(X1 + X2 + X3) = Sigma 1^2 + Sigma 2^2 + Sigma 3^2

= 20 + 20 + 20

= 60

To find the variance of X1 + X2 - X3, you can use the formula for the variance of differences in independent random variables.

Var(X1 + X2 - X3) = Var(X1) + Var(X2) + Var(X3)

= Sigma 1^2 + Sigma 2^2 + Sigma 3^2

= 20 + 20 + 20

= 60

So the answer is C) 60.

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