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X 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?

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SSC CGL JSO Tier-II, 2018 (Statistics) Official Paper-III (Held On: 14 Sept, 2019)
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  1. N(130, 7)
  2. N(130, 3)
  3. N(130, 5)
  4. N(130, 4)

Answer (Detailed Solution Below)

Option 3 : N(130, 5)
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Detailed Solution

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Given

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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