GATE DS&AI 2024 | Question: 1

Question

​​​​Consider the following statements:

1. The mean and variance of a Poisson random variable are equal.
2. For a standard normal random variable, the mean is zero and the variance is one.

Which ONE of the following options is correct?

• A. Both $\text{(i)}$ and $\text{(ii)}$ are true
• B. $\text{(i)}$ is true and $\text{(ii)}$ is false
• C. $\text{(ii)}$ is true and $\text{(i)}$ is false
• D. Both $\text{(i)}$ and $\text{(ii)}$ are false

Answer 1

Let's evaluate each statement:

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

For a Poisson random variable \( X \) with parameter \( \lambda \), the mean (expected value) and variance are both equal to \( \lambda \).

So, statement (i) is true.

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

A standard normal random variable has a mean of zero and a variance of one. This property defines the standard normal distribution.

So, statement (ii) is true.

Therefore, the correct option is:

A. Both (i) and (ii) are true