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Questions › GATE › GATE 2025 › Q50
2 marks, −0.667Statistics › Random variables and standard distributions › Expectation and varianceHardabout 2 min

GATE 2025 Question 50: Random variables and standard distributions

Let X1,X2,X3,…X_1, X_2, X_3, \ldotsX1​,X2​,X3​,…, be independent and identically distributed random variables with E[X1]=μE[X_1]=\muE[X1​]=μ.

Let NNN be a positive integer valued random variable with E[N]=nE[N]=nE[N]=n.

If SN=X1+X2+⋯+XNS_N = X_1+X_2+\cdots+X_NSN​=X1​+X2​+⋯+XN​, then E[SN]=E[S_N] =E[SN​]=

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Let X₁, X₂, X₃, …, be independent and identically distributed random variables with E[X₁]=μ. Let N be a positive integer valued random variable with E[N]=n. If S_N = X₁+X₂+⋯+X_N, then E[S_N] = (A) μ (B) Nμ (C) nμ (D) μⁿ

Also written as: Let X_1, X_2, X_3,..., be independent and identically distributed random variables with E[X_1]=mu. Let N be a positive integer valued random variable with E[N]=n. If S_N = X_1+X_2+...+X_N, then E[S_N] =

Random variables and standard distributions has come up 173 times in 7 exams since 2005.

What this question tests

This question is on Expectation and variance, part of Random variables and standard distributions in Statistics.

The mean and spread of a random variable, and how they change under transformations and sums.

TestStop has 50 past-paper questions on this subtopic; the nearest in year are below.

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Question from the GATE 2025 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.