GATE DA 2024 Q11: Mean and variance of Poisson and standard normal

Consider the following statements:

(i) The mean and variance of a Poisson random variable are equal.

(ii) For a standard normal random variable, the mean is zero and the variance is one.

Which ONE of the following options is correct?

Try it: multiple choice: exactly one correct option

Wrong answer costs 1/3 mark in GATE.

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Answer: A (official GATE 2024 final answer key)

Concept used: Moments of standard distributions: Poisson( $\lambda$ ) has mean $=$ variance $=\lambda$ ; $N(0,1)$ has mean 0 and variance 1.

First step: Recall the definitions: both statements are standard facts.

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Source: official GATE 2024 DA question paper and final answer key, organised by IISc Bangalore. Question paper · Answer key