The GATE Grind

GATE 2024 DA – Question 11

Probability and Statistics · Random variables, discrete and continuous distributions · 1 mark · Multiple choice

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?

  1. Both (i) and (ii) are true
  2. (i) is true and (ii) is false
  3. (ii) is true and (i) is false
  4. Both (i) and (ii) are false

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Show answer and explanation

Correct answer: (A) Both (i) and (ii) are true

Explanation

A Poisson variable with parameter $\lambda$ has mean $\lambda$ and variance $\lambda$. The standard normal variable is defined to have mean 0 and variance 1. Both statements are true.