# Thread: S^2 is variance of sample from normal distribution - what is distribution of cS^2?

1. ## S^2 is variance of sample from normal distribution - what is distribution of cS^2?

If $S^2$ is the variance of a random sample which is drawn from a normal distribution $N(\mu,\sigma^2)$ then $cS^2$ has a standard distribution for a particular value of the constant c.

Specify the constant c. What is the distribution?

How many pairs of positive constants a; b exist such that $P(a < cS^2 < b) = 0.95$?

2. Originally Posted by Amanda1990
If $S^2$ is the variance of a random sample which is drawn from a normal distribution $N(\mu,\sigma^2)$ then $cS^2$ has a standard distribution for a particular value of the constant c.

Specify the constant c. What is the distribution?

How many pairs of positive constants a; b exist such that $P(a < cS^2 < b) = 0.95$?
You're expected to know (or find out eg. Variance - Wikipedia, the free encyclopedia) that $\frac{(n-1) S^2}{\sigma^2}$ ~ $\chi^2_{n-1}$.

Use this to answer the second part of your question.

3. I see! Thing is, surely the answer to the second part of the question is "infinitely many"? Do you think we're supposed to identify all the possible intervals [a,b]?

4. Originally Posted by Amanda1990
I see! Thing is, surely the answer to the second part of the question is "infinitely many"? Do you think we're supposed to identify all the possible intervals [a,b]?
Answer the question as asked (explain why that is the answer).

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