# T Distribution

This is a continuous distribution.
Also known as the Students T Distribution
This is probably the second most commonly used probability distribution function.
The normal convention for representing the T distribution is to use a lower case "t".
The T distribution is often used when you have a small sample size.
When the sample size is small and the standard deviation of the population is not known you need to use the T distribution as opposed to the normal distribution.
You can almost think of the normal distribution as a special case of the t distribution when sample sizes are large (over 50 etc)

### Properties

Continuous
right tail
has a family specified by the "degrees of freedom" value
one tail - one sides
two tails - two sided

SS

SS

### Excel Functions

Returns
T.DIST(x, degrees_freedom, tails) - (Replaces TDIST)

T.DIST.2T(x, degrees_freedom)

TDIST(t, dt, 2) - Two sided p value for t statistic where v is the degress of freedom.

T.DIST.RT(x, degrees_freedom)

TDIST(t, dt, 1)

T.INV(probability, degrees_freedom)

T.INV.2T(probability, degrees_freedom) - (Replaces TINV)

### Important

The function T.INV.RT does not exist.