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

• Feb 5th 2009, 08:57 AM
Amanda1990
S^2 is variance of sample from normal distribution - what is distribution of cS^2?
If $\displaystyle S^2$ is the variance of a random sample which is drawn from a normal distribution $\displaystyle N(\mu,\sigma^2)$ then $\displaystyle cS^2$ 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 $\displaystyle P(a < cS^2 < b) = 0.95$?
• Feb 5th 2009, 04:15 PM
mr fantastic
Quote:

Originally Posted by Amanda1990
If $\displaystyle S^2$ is the variance of a random sample which is drawn from a normal distribution $\displaystyle N(\mu,\sigma^2)$ then $\displaystyle cS^2$ 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 $\displaystyle P(a < cS^2 < b) = 0.95$?

You're expected to know (or find out eg. Variance - Wikipedia, the free encyclopedia) that $\displaystyle \frac{(n-1) S^2}{\sigma^2}$ ~ $\displaystyle \chi^2_{n-1}$.