## Properties of t distribution, Mathematics

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Properties of t distribution

1. The t distribution ranges from - ∞ to ∞ first as does the general distribution

2. The t distribution as the standard general distribution is bell shaped and symmetrical around mean zero

3. The shapes of the t distribution changes like the number of degrees of freedom changes

4. The t distribution is more platykurtic that the normal distribution

5. The t distribution has a greater dispersion than the standard general distribution. Like n gets larger the t distribution approaches the general distribution while n = 30 the difference is extremely small

Relation among the t distribution and standard general distribution is displayed in the given diagram Note that the t distribution has different shapes depending on the size of the sample. When the sample is rather small the height of the t distribution is shorter than the general distribution and the tails are wider.

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