The t-distribution is a symmetrical bell-shaped probability distribution defined by a single parameter known as degrees of freedom. The distribution will be different for each degree of freedom.
Degrees of freedom: The degrees of freedom equals the total number of independent variables that can vary freely. In the calculation of sample variance, the numerator uses the sample mean. So, for a total n number of observations, only n-1 observations can move freely because one observation won't be able to move freely to make the mean equal to the sample mean. The t-distribution for sample mean also has a degree of freedom as n-1 for a sample size of n.
The standard normal distribution has thinner tails as compared to t-distribution i.e. its tails approach zero faster than the t-distribution. As the degrees of freedom increases, the t-distribution approaches the standard normal distribution.
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