I think the Fermi-Dirac statistic is referring to the Fermi-Dirac distribution function:

$$f(E) = \frac{1}{1+\exp\left(\frac{E-\mu}{kT} \right)},$$

and this function does not exceed one, meaning you never have more than one particle in a certain quantum state, unlike in the case of the Bose-Einstein distribution function.

The quantum state is always defined in terms of quantum numbers, and the spin is always one of the well defined quantum numbers.

Do you want to know how comes that half-integer spin is related to such a distribution function?

In general, half-integer spin -> Pauli exclusion principle -> Fermi-Dirac distribution function.

The relationship half-integer spin -> Pauli exclusion principle is described here: https://en.wikipedia.org/wiki/Spin-statistics_theorem

The link Pauli exclusion principle -> Fermi-Dirac distribution function is described here: https://nanohub.org/resources/5787/download/2009.02.02-ECE606-L9.pdf

I think the Fermi-Dirac statistic is referring to the Fermi-Dirac distribution function:

$$f(E) = \frac{1}{1+\exp\left(\frac{E-\mu}{kT} \right)},$$

and this function does not exceed one, meaning you never have more than one particle in a certain quantum state, unlike in the case of the Bose-Einstein distribution function.

The quantum state is always defined in terms of quantum numbers, and the spin is always one of the well defined quantum numbers.

Do you want to know how comes that half-integer spin is related to such a distribution function?

In general, half-integer spin -> Pauli exclusion principle -> Fermi-Dirac distribution function.

The relationship half-integer spin -> Pauli exclusion principle is described here: https://en.wikipedia.org/wiki/Spin-statistics_theorem

The link Pauli exclusion principle -> Fermi-Dirac distribution function is described here: https://nanohub.org/resources/5787/download/2009.02.02-ECE606-L9.pdf

I think the Fermi-Dirac statistic is referring to the Fermi-Dirac distribution function:

$$f(E) = \frac{1}{1+\exp\left(\frac{E-\mu}{kT} \right)},$$

and this function does not exceed one, meaning you never have more than one particle in a certain quantum state, unlike in the case of the Bose-Einstein distribution function.

The quantum state is always defined in terms of quantum numbers, and the spin is always one of the well defined quantum numbers.

Do you want to know how comes that half-integer spin is related to such a distribution function?

I think the Fermi-Dirac statistic is referring to the Fermi-Dirac distribution function:

$$f(E) = \frac{1}{1+\exp\left(\frac{E-\mu}{kT} \right)},$$

and this function does not exceed one, meaning you never have more than one particle in a certain quantum state, unlike in the case of the Bose-Einstein distribution function.

The quantum state is always defined in terms of quantum numbers, and the spin is always one of the well defined quantum numbers.

Do you want to know how comes that half-integer spin is related to such a distribution function?

In general, half-integer spin -> Pauli exclusion principle -> Fermi-Dirac distribution function.

The relationship half-integer spin -> Pauli exclusion principle is described here: https://en.wikipedia.org/wiki/Spin-statistics_theorem

The link Pauli exclusion principle -> Fermi-Dirac distribution function is described here: https://nanohub.org/resources/5787/download/2009.02.02-ECE606-L9.pdf