Show how the variance decrease as degrees of freedom/sample size get bigger

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rogo0034
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Homework Statement


TNtoZ.png



Homework Equations



XY0kG.png


The Attempt at a Solution



I'm confused actually how to go about this. Sounds very simple, but when i do what they suggest, 'first, find the variance of (n-1)s2/σ2

i get larger variances rather than smaller, which makes no sense. should i be using the chart for this? (below)

uhT2u.png
 

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rogo0034 said:

Homework Statement


TNtoZ.png



Homework Equations



XY0kG.png


The Attempt at a Solution



I'm confused actually how to go about this. Sounds very simple, but when i do what they suggest, 'first, find the variance of (n-1)s2/σ2

i get larger variances rather than smaller, which makes no sense. should i be using the chart for this? (below)

uhT2u.png

Since you don't tell us what the chart represents, it is impossible to tell if it is relevant or not; I suspect not.

You are told that [itex]V = (n-1)S^2/\sigma^2[/itex] has a Chi-squared distribution with (n-1) degrees of freedom. Do you know the variance formula for the Chi-squared distribution? (It is readily available.)

RGV