Question
Download Solution PDFX and Y are independent normal variables with mean 50 and 80 respectively and standard deviation as 4 and 3 respectively. What is the distribution of X + Y?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven
X and Y are independent normal variables with
Mean (X) = 50
Mean (Y) = 80
SD (σx) = 4
SD(σy) = 3
Concept
Normal distribution is indicated by N(μ, √(σ2x+ σ22))
Calculation
Since X and Y are independent then
⇒ Z = X + Y ~ N(X + Y, (σ2x + σ2y)
⇒ P(Z) = P(X + Y) ~ N(130, (42 + 32)
⇒ N(130, 25)
∴ N(μ, √(σ2x+ σ22) is N(130, 5)
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