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Questions › GATE › GATE 2026 › Q47
2 marks, −0.667Statistics › Sampling distributions and limit theorems › Sampling distributions of the mean and proportionModerateabout 2 min

GATE 2026 Question 47: Sampling distributions and limit theorems

Suppose that X1,X2,X3X_1,X_2,X_3X1​,X2​,X3​ and X4X_4X4​ are independent random variables with common distribution N(4,12)N(4,12)N(4,12). Observations x1=6,x2=3,x3=1x_1=6,x_2=3,x_3=1x1​=6,x2​=3,x3​=1, and x4=10x_4=10x4​=10 correspond to X1,X2,X3X_1,X_2,X_3X1​,X2​,X3​ and X4X_4X4​, respectively. What is the sample mean and its sampling distribution?

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Plain-text version

Suppose that X₁,X₂,X₃ and X₄ are independent random variables with common distribution N(4,12). Observations x₁=6,x₂=3,x₃=1, and x₄=10 correspond to X₁,X₂,X₃ and X₄, respectively. What is the sample mean and its sampling distribution? (A) 4 and N(4,3) (B) 5 and N(4,3) (C) 4 and N(5,12) (D) 5 and N(4,12)

Also written as: Suppose that X_1,X_2,X_3 and X_4 are independent random variables with common distribution N(4,12). Observations x_1=6,x_2=3,x_3=1, and x_4=10 correspond to X_1,X_2,X_3 and X_4, respectively. What is the sample mean and its sampling distribution?

Sampling distributions and limit theorems has come up 25 times in 7 exams since 2007.

What this question tests

This question is on Sampling distributions of the mean and proportion, part of Sampling distributions and limit theorems in Statistics.

How sample statistics vary from sample to sample and how precisely they estimate.

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