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Student T Distribution
The Student t distribution with n
degrees of freedom is the continuous probability distribution
with the following probability density function:
The notation X ~ Tn denotes that the random
variable X has a Student t distribution with n degrees
of freedom. The random variable X is also the quotient of two
independent random variables, the dividend being a standard
normal variable and the divisor the square root of a random
variable with a chi-square distribution with n degrees
of freedom divided by n. That is, if Z and Y are
independent,
The Student t distribution with n degrees of freedom
has a graph that is symmetric about the y-axis and is very
similar to that of the standard normal distribution. However, its
graph flatter than that of the standard normal distribution, with
more area in its tails. But as n increases, the Student
t distribution converges to the standard normal distribution.
The Upper Percentiles of the Student's t-Distribution Tables
of any Statistics book tabulates the values of upper percentiles
for the Student t distribution with n degrees of freedom, for
selected values of n from 1 to 120. Since the Student t
distribution has a symmetric distribution about x = 0, the values
of its lower percentiles can be derived from the values of its
upper percentiles. For X ~ Tn,
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