Question: The question is incomplete. What need to be calculated is not included in the question. Below is the question requirement and the answer.
a) Suppose X1, X2, and X3 are independent. All three repairs must be completed on a given object. What is the mean and variance of the total repair time for this object?
Answer:
Mean = 50 minutes
Variance = 725 minutes
Explanation:
X₁ = 50
X₂ = 60
X₃ = 40
σ₁ = 15
σ₂ = 20
σ₃ = 10
Calculating the mean E(Y) using the formula;
E(Y) = E(X₁ +X₂ +X₃)/3
= (EX₁ + EX₂ + EX₃)/3
= (50 + 60 + 40)/3
= 50 minutes
Therefore, the mean of the total repair time for this object is 50 minutes
Calculating the variance V(Y) using the formula;
V(Y) = V(X₁ +X₂ +X₃)
= E(X₁) +E(X₂) + E(X₃)
= σ₁² + σ₂² + σ₃²
= 15² + 20² + 10²
= 225 + 400 + 100
= 725 minutes
Therefore, the variance of the total repair time for this object is 725 minutes