Question

If Y follows Chi-square distribution with 16 degrees of freedom. Then mean of Y is

• A. 16
• B. 4
• C. 32
• D. 196

Hint:

For any Chi-square distribution, the Mean is simply equal to the degrees of freedom ($k$), and the Variance is double the degrees of freedom ($2k$).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The Chi-square ($\chi^2$) distribution is a continuous probability distribution defined by its degrees of freedom parameter.
Key Formula or Approach:
For a Chi-square random variable $Y$ with $k$ degrees of freedom:
\[ \text{Mean}(Y) = k \]
\[ \text{Variance}(Y) = 2k \]

Step 2: Detailed Explanation:
We are given:
Degrees of freedom, $k = 16$
Using the fundamental property of the Chi-square distribution, the mean is equal to the degrees of freedom:
\[ \text{Mean}(Y) = 16 \]
Therefore, the mean of the distribution is 16.

Step 3: Final Answer
The correct option is (A).